
Valentina TADDEI
Professore Associato Dipartimento di Scienze e Metodi dell'Ingegneria

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2022
 Bound Sets Approach to Impulsive Floquet Problems for Vector SecondOrder 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 secondorder 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 upperCarathéodory righthand sides are investigated and it is shown afterwards how can the conditions be simplified in more regular case of upper semicontinuous 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 C1bounding functions with locally Lipschitzian gradients are considered at first and it is shown afterwards how the conditions change in case of C2bounding functions. The paper concludes with an application of obtained results to Liénardtype 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 SecondOrder 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 semilinear secondorder 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 righthand 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–Taylortype damping term.
2021
 Lpexact 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 finitedimensional 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 integrodifferential inclusions with nondensely 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 integrodifferential inclusion in a Banach space with a nondensely 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 noncompactness 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 GlicksbergKy 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 secondorder 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 secondorder 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 ScorzaDragoni type result. Since the related bounding (Liapunovlike) 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 upperCarathéodory righthand 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 upperCarathéodory
righthand 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 multipoint 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 integrodifferential 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. Lyapunovlike 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 reactiondiffusion 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 integropartial 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 Hartmantype inequality and it involves a ScorzaDragoni 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 integrodifferential 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 halflinear 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 nonoscillatory halflinear differential equation of the form (r(t)y'^ {alpha1} sgn y')'=p(t)y^{alpha1}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, antiperiodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragonitype result for multivalued maps. The conclusions are original also in the singlevalued 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 integropartialdifferential 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 integrodifferential 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 onedimensional 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
reactiondiffusion 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 agepopulation 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 integrodifferential
equation arising in agestructure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.
2012
 Erratum and addendum to "Twopoint 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 BenedettiMalagutiTaddei, 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 Banach spaces with the RadonNikodym 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 Liapunovlike technique and a ScorzaDragoni 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
 Twopoint b.v.p. for multivalued equations with weakly regular r.h.s.
[Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract
A twopoint 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. Lyapunovlike 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 integrodifferential 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 Lyapunovlikefunction, 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 firstorder 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
 Twopoints 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 upperCaratheodory differential inclusions by means of strictly localized C2bounding 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 twopoints 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 nonsmooth 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 nonoscillatory solutions of quasi linear ordinary differential equations
[Articolo su rivista]
Malaguti, Luisa; Taddei, Valentina
abstract
The paper deals with a quasilinear ordinarydifferential equation when the nonlinearity is not necessarily monotone in its second argument. We find necessary and sufficient conditions for the existence of unbounded nonoscillatory 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 nonoscillatory 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 secondorder 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 Lyapunovlike 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 twopoints boundary conditions
[Articolo su rivista]
Taddei, Valentina
abstract
We consider differential equations with linear twopoints 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 C1class of Liapunovlike 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 complexvalued polynomial coefficients is investigated by means of a continuation principle.
2000
 Bound sets for Floquet boundary value problems: the nonsmooth 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