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Valentina TADDEI

Professore Associato
Dipartimento di Scienze e Metodi dell'Ingegneria


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Pubblicazioni

2022 - Bound Sets Approach to Impulsive Floquet Problems for Vector Second-Order Differential Inclusions [Articolo su rivista]
Pavlackova, M.; Taddei, V.
abstract

In this paper, the existence and the localization of a solution of an impulsive vector multivalued second-order Floquet boundary value problem are investigated. The method used in the paper is based on the combination of a fixed point index technique with bound sets approach. At first, problems with upper-Carathéodory right-hand sides are investigated and it is shown afterwards how can the conditions be simplified in more regular case of upper semi-continuous right hand side. In this more regular case, the conditions ensuring the existence and the localization of a solution are put directly on the boundary of the considered bound set. This strict localization of the sufficient conditions is very significant since it allows some solutions to escape from the set of candidate solutions. In both cases, the C1-bounding functions with locally Lipschitzian gradients are considered at first and it is shown afterwards how the conditions change in case of C2-bounding functions. The paper concludes with an application of obtained results to Liénard-type equations and inclusions and the comparisons of our conclusions with the few results related to impulsive periodic and antiperiodic Liénard equations are obtained.


2022 - Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces [Articolo su rivista]
Pavlackova, M.; Taddei, V.
abstract

In this paper, the existence of a mild solution to the Cauchy problem for impulsive semi-linear second-order differential inclusion in a Banach space is investigated in the case when the nonlinear term also depends on the first derivative. This purpose is achieved by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables obtaining the result under easily verifiable and not restrictive conditions on the impulsive terms, the cosine family generated by the linear operator and the right-hand side while avoiding any requirement for compactness. Firstly, the problems without impulses are investigated, and then their solutions are glued together to construct the solution to the impulsive problem step by step. The paper concludes with an application of the obtained results to the generalized telegraph equation with a Balakrishnan–Taylor-type damping term.


2021 - Lp-exact controllability of partial differential equations with nonlocal terms [Articolo su rivista]
Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina
abstract

The paper deals with the exact controllability of partial differential equations by linear controls. The discussion takes place in infinite dimensional state spaces since these equations are considered in their abstract formulation as semilinear equations. The linear parts are densely defined and generate strongly continuous semigroups. The nonlinear terms may also include a nonlocal part. The solutions satisfy nonlocal properties, which are possibly nonlinear. The states belong to Banach spaces with a Schauder basis and the results exploit topological methods. The novelty of this investigation is in the use of an approximation solvability method which involves a sequence of controllability problems in finite-dimensional spaces. The exact controllability of nonlocal solutions can be proved, with controls in Lp spaces, 1<∞. The results apply to the study of the exact controllability for the transport equation in arbitrary Euclidean spaces and for the equation of the nonlinear wave equation.


2021 - On solvability of the impulsive Cauchy problem for integro-differential inclusions with non-densely defined operators [Articolo su rivista]
Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina
abstract

We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space.


2020 - Evolution fractional differential problems with impulses and nonlocal conditions [Articolo su rivista]
Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina
abstract

We obtain existence results for mild solutions of a fractional differential inclusion subjected to impulses and nonlocal initial conditions. By means of a technique based on the weak topology in connection with the Glicksberg-Ky Fan Fixed Point Theorem we are able to avoid any hypothesis of compactness on the semigroup and on the nonlinear term and at the same time we do not need to assume hypotheses of monotonicity or Lipschitz regularity neither on the nonlinear term, nor on the impulse functions, nor on the nonlocal condition. An application to a fractional diffusion process complete the discussion of the studied problem


2020 - On the impulsive Dirichlet problem for second-order differential inclusions [Articolo su rivista]
Pavlačková, Martina; TADDEI, Valentina
abstract

Solutions in a given set of an impulsive Dirichlet boundary value problem are investigated for second-order differential inclusions. The method used for obtaining the existence and the localization of a solution is based on the combination of a fixed point index technique developed by ourselves earlier with a bound sets approach and Scorza-Dragoni type result. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets.


2019 - A bounding function approach to impulsive Dirichlet problem with an upper-Carathéodory right-hand side [Articolo su rivista]
Pavlackova, Martina; Taddei, Valentina
abstract

In this article, we prove the existence and localization of solutions for a vector impulsive Dirichlet problem with multivalued upper-Carathéodory right-hand side. The result is obtained by combining the continuation principle with a bound sets technique. The main theorem is illustrated by an application to the forced pendulum equation with viscous damping term and dry friction coecient.


2019 - Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions [Articolo su rivista]
Malaguti, Luisa; Rykaczewski, Krzysztof; Taddei, Valentina
abstract

The paper deals with semilinear evolution equations in Banach spaces. By means of linear control terms, the controllability problem is investigated and the solutions satisfy suitable nonlocal conditions. The Cauchy multi-point condition and the mean value condition are included in the present discussion. The final configuration is always achieved with a control with minimum norm. The results make use of fixed point techniques; two different approaches are proposed, depending on the use of norm or weak topology in the state space. The discussion is completed with some applications to dynamics of diffusion processes.


2019 - Exact controllability of infinite dimensional systems with controls of minimal norm [Articolo su rivista]
Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina
abstract

The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimen- sional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.


2019 - Nonlocal solutions of parabolic equations with strongly elliptic differential operators [Articolo su rivista]
Benedetti, Irene; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction–diffusion processes in several frameworks. A linear diffusion term in divergence form is included which generates a strongly elliptic differential operator. A further linear part, of integral type, is present which accounts of nonlocal diffusion behaviours. The main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions. The Cauchy multipoint and the mean value conditions are included in this investigation. The problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the Leray–Schauder topological degree. A bounding function (i.e. Lyapunov-like function) theory is developed, which is new in this infinite dimensional context. It allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument.


2017 - An approximation solvability method for nonlocal semilinear differential problems in Banach spaces [Articolo su rivista]
Benedetti, Irene; Loi, Nguyen Van; Taddei, Valentina
abstract

A new approximation solvability method is developed for the study of semilinear differential equations with nonlocal conditions without the compactness of the semigroup and of the nonlinearity. The method is based on the Yosida approximations of the generator of C0semigroup, the continuation principle, and the weak topology. It is shown how the abstract result can be applied to study the reaction-diffusion models.


2017 - Nonlocal diffusion second order partial differential equations [Articolo su rivista]
Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with a second order integro-partial differential equation in RnRn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.


2017 - On generalized boundary value problems for a class of fractional differential inclusions [Articolo su rivista]
Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina
abstract

We prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.


2016 - Semilinear delay evolution equations with measures subjected to nonlocal initial conditions [Articolo su rivista]
Benedetti, I.; Malaguti, Luisa; Taddei, Valentina; Vrabie, I. I.
abstract

We prove a global existence result for bounded solutions to a class of abstract semilinear delay evolution equations with measures subjected to nonlocal initial data of the form: du(t)={Au(t)+f(t,u t )}dt+dg(t) with t∈R+ and u(t)=h(u)(t) for t∈[−τ,0], with τ≥0. The operator A:D(A)⊆X→X is the infinitesimal generator of a C0 -semigroup, f:R+ ×R([−τ,0];X)→X is continuous, g∈BVloc (R+ ;X) and h:Rb (R + ;X)→R([−τ,0];X) is nonexpansive.


2016 - Solutions of half-linear differential equations in the classes Gamma and Pi [Articolo su rivista]
Rehak, Pavel; Taddei, Valentina
abstract

We study asymptotic behavior of (all) positive solutions of the non-oscillatory half-linear differential equation of the form (r(t)|y'|^ {alpha-1} sgn y')'=p(t)|y|^{alpha-1}sgn y, where alpha>1 and r,p are positive continuous functions, with the help of the Karamata theory of regularly varying functions and the de Haan theory. We show that increasing resp. decreasing solutions belong to the de Haan class Gamma resp. Gamma- under suitable assumptions. Further we study behavior of slowly varying solutions for which asymptotic formulas are established. Some of our results are new even in the linear case alpha=2.


2015 - Nonlocal problems in Hilbert spaces [Relazione in Atti di Convegno]
Benedetti, Irene; Malaguti, Luisa; Taddei, Valentina
abstract

An existence result for differential inclusions in a separable Hilbert space is furnished. A wide family of nonlocal boundary value problems is treated, including periodic, anti-periodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragoni-type result for multivalued maps. The conclusions are original also in the single-valued setting. An application to a nonlocal dispersal model is given.


2015 - On noncompact fractional order differential inclusions with generalized boundary condition and impulses in a Banach space [Articolo su rivista]
Benedetti, Irene; Obukovskii, Valeri; Taddei, Valentina
abstract

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.


2014 - Controllability for systems governed by semilinear evolution equations without compactness [Articolo su rivista]
Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina
abstract

We study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation.


2013 - Evolution Problems with Nonlinear Nonlocal Boundary Conditions [Articolo su rivista]
Irene, Benedetti; Taddei, Valentina; Martin, Vath
abstract

We provide a new approach to obtain solutions of evolution equations with nonlinear and nonlocal in time boundary conditions. Both, compact and noncompact semigroups are considered. As an example we show a “principle of huge growth”: every control of a reaction-diffusion system necessarily leads to a profile preserving nonlinear huge growth for an appropriate initial value condition. As another example we apply the approach with noncompact semigroups also to a class of age-population models, based on a hyperbolic conservation law.


2013 - Nonlocal semilinear evolution equations without strong compactness: theory and applications [Articolo su rivista]
Irene, Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. No strong compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. A wide family of nonlocal associated boundary value problems is investigated by means of a fixed point technique. Applications are given to an optimal feedback control problem, to a nonlinear hyperbolic integro-differential equation arising in age-structure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.


2012 - Erratum and addendum to "Two-point b.v.p. for multivalued equations with weakly regular r.h.s." [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

In this paper, we define a topological index for compact multivalued maps in convex metrizable subsets of a locally convex topological vector space in order to correct the proofs of Theorems 4.1 and 4.2 in Benedetti-Malaguti-Taddei, Nonlinear Anal. 74 (2011) 3657–3670.


2012 - Semilinear evolution equations in abstract spaces and applications [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive Banach space. Weakly compact valued nonlinear terms are considered, combined with strongly continuous evolution operators generated by the linear part. A continuation principle or a fixed point theorem are used, according to the various regularity and growth conditions assumed. Applications to the study of parabolic and hyperbolic partial differential equations are given.


2011 - Boundary value problem for differential inclusions in fréchet spaces with multiple solutions of the homogeneous problem [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with the multivalued boundary value problemx' Є A(t, x)x + F(t, x) for a.a. t Є [a, b], Mx(a)+Nx(b) = 0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x. We prove the existenceof global solutions in the Sobolev space W1,p([a, b], E) with 1 < p < ∞ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneouslinearized problem. An example completes the discussion.


2011 - Strictly localized bounding functions and Floquet boundary value problems [Articolo su rivista]
S., Cecchini; MALAGUTI, Luisa; TADDEI, Valentina
abstract

Semilinear multivalued equations are considered, in separable Ba-nach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable.


2011 - Two-point b.v.p. for multivalued equations with weakly regular r.h.s. [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusionsappearing in dispersal population models. Comparisons are included, with recent related achievements.


2010 - BVP for Carathéodory inclusions in Hilbert spaces: sharp existence conditions and applications [Articolo su rivista]
I., Benedetti; E., Panasenko; Taddei, Valentina
abstract

This article concernsan existence result for Floquet boundary value problems associatedto semilinear differential inclusions with Carathéodory righthand side in a Hilbert space. We apply a continuation principleand we require a sharp (i.e., localized on the boundary)transversality condition. We give an application to a nonlinearpartial differential inclusion with periodic conditions


2010 - Semilinear differential inclusions via weak topologies [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with the multivalued initial value problem x'(t) Є A(t, x)x+ F (t, x) for a.a. t in[a, b], x(a) = x_0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have asuperlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p ([a, b], E) with 1 < p < ∞. Introducing a suitably defined Lyapunov-likefunction, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushingcondition in two different ways. Some examples complete the discussion.


2009 - On boundary value problems in Banach spaces [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with boundary value problemsassociated to first-order differential inclusions in Banach spaces. The solvability is investigated in the (strong) Carathèodory sense on compact intervals. To this aim, we develop a general method that relies on degree arguments. This method is still combined with a bound sets technique for checking the behavior of trajectories in the neighborhood of a suitable parametric set of candidate solutions. On this basis, we obtain effective criteria for the existence of solutions of Floquet problems. The existence of entirely bounded solutions is also established by means of a sequence of solutions on compact increasing intervals.


2008 - Two-points boundary value problems for Carathèodory second order equations [Articolo su rivista]
Taddei, Valentina
abstract

Using a suitable version of Mawhin's continuation principle, we obtains an existence result for the Floquet boundary value problem for second order Carathèodory differential equations by means of strictly localized C^2 bounding functions


2007 - A bounding functions approach to multivalued boundary value problems [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

The solvability of Floquet boundary value problems is investigated for upper-Caratheodory differential inclusions by means of strictly localized C-2-bounding functions. The existence of an entirely bounded solution is obtained in a sequential way. Our criteria can be regarded as a multivalued extension of recent results of Mawhin and Thompson concerning periodic and bounded solutions of Caratheodory differential equations. A simple illustrating example is supplied.


2007 - Bound sets and two-points boundary value problems for second order differential equations [Articolo su rivista]
Taddei, Valentina; Zanolin, F.
abstract

Using Mawhin's continuation principle we obtain a general result on the existence ofsolutions to a boundary value problem for vector second order nonlinear ODEs.Applications are given to the existence of solutions which are containedin suitable bound sets with possibly non-smooth boundary.


2007 - Existence of positive decaying solutions for nonlinear singular second order equations [Articolo su rivista]
Rehak, P; Taddei, Valentina
abstract

We study a singular boundary value problem for a second order equations under quite general assumptions. The conditions guaranteeing its solvability are given, which yield some of the existing results when the equation reduces to special forms.


2005 - Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations [Articolo su rivista]
Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with a quasi-linear ordinarydifferential equation when the nonlinearity is not necessarily monotone in its second argument. We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. In some special cases we are able to show the exact asymptotic growth of these solutions. We apply previous analysis for studying the non-oscillatory problem. Several examples are included.


2005 - Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations [Articolo su rivista]
Papini, D; Taddei, Valentina
abstract

Delayed neural networks with periodic coefficients and discontinuous and/or unbounded activation functions are investigated by means of Lyapunov theory and fixed point theorems. We obtain conditions, independent from the delay, assuring the existence of an unique limit cycle, which is globally exponential stable.


2004 - Bounded solutions and wavefronts for discrete dynamics [Articolo su rivista]
Malaguti, Luisa; P., Rehak; Taddei, Valentina
abstract

This paper deals with the second-order nonlinear difference equation Delta(r(k)Deltau(k)) + q(k)g(u(k+1)) = 0 where {r(k)} and {q(k)} are positive real sequences defined on N, and the nonlinearity g : R --> R is nonnegative and nontrivial. Sufficient and necessary conditions are given, for the existence of bounded solutions starting from a fixed initial condition u(0). The same dynamic, with f instead of g such that uf (u) > 0 for u not equal 0, was recently extensively investigated. On the contrary, our nonlinearity g is of a small appearance in the discrete case. Its introduction is motivated by the analysis of wavefront profiles in biological and chemical models. The paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f. Some applications in the study of wavefronts complete this work.


2003 - Bounded solutions of Carathéodory differential inclusions: a bound sets approach [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

A bound sets technique is developed for Floquet problems to Carathèodory differential inclusions. It relies on the construction of either continuous or locally Lipschitzian Lyapunov-like bounding functions. Proceeding sequentially, the existence of bounded trajectories is then obtained. Nontrivial examples are supplied to illustrate our approach.


2002 - Bound sets for first order differential equations with general linear two-points boundary conditions [Articolo su rivista]
Taddei, Valentina
abstract

We consider differential equations with linear two-points boundary conditions. We present some existence results for bound sets defined as the intersection of sublevel sets of particular scalar functions, called bounding functions. All the three cases, namely continuous, locally lipschitzian and $ C^1-$class bounding functions, are analized. Comparisons with previous results are given. Finally we apply the existence theorems to the homogeneous Cauchy problem and to the Picard problem


2001 - Floquet Boundary Value Problems for Differential Inclusions: a Bound Sets Approach [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

A technique is developed for the solvability of the Floquet boundary value problem associated to a differential inclusion. It is based on the usage of a not necessarily C-1-class of Liapunov-like bounding functions. Certain viability arguments are applied for this aim. Some illustrating examples are supplied.


2001 - Periodic solutions for certain systems of planar complex polynomial equations [Articolo su rivista]
Taddei, Valentina
abstract

The existence of periodic solutions of a planar system with complex-valued polynomial coefficients is investigated by means of a continuation principle.


2000 - Bound sets for Floquet boundary value problems: the non-smooth case [Articolo su rivista]
Taddei, Valentina
abstract

A definition of bound set for boundary value problems is given. Sufficient conditions are given in order to obtain a bound set for Floquet boundary value problems, as intersection of sublevel sets of not necessarily $ C^1 $ bounding functions


1998 - Asymptotic properties of an ordinary differential equation via topological methods [Articolo su rivista]
Malaguti, Luisa; Taddei, Valentina
abstract

The existence of bounded and unbounded solutions for a second order equation is obtained via topological methods