Inclusions In Banach Spaces Research Articles

Existence Results for Impulsive Multivalued Semilinear Neutral Functional Differential Inclusions in Banach Spaces

In this paper, the existence of mild solutions for first- and second-order impulsive semilinear neutral functional differential inclusions in Banach spaces is investigated. The results are obtained by using a fixed point theorem for condensing multivalued maps due to Martelli and semigroup theory.

Existence and approximation of solutions for set-valued variational inclusions in Banach space

Existence and approximation of solutions for set-valued variational inclusions in Banach space

Nonlocal Cauchy Problems for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

In this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces with nonlocal conditions. The results are obtained by using a fixed point theorem for condensing maps due to Martelli.

A new class of generalized set-valued implicit variational inclusions in banach spaces with an application

In this paper, we introduce and study a new class of generalized set-valued implicit variational inclusions in real Banach spaces. By using Nadler's Theorem and the resolvent operator technique for m-accretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this class of generalized set-valued implicit variational inclusions. We prove the existence of solution for this kind of generalized set-valued implicit variational inclusions without compactness and the convergence of iterative sequences generated by the algorithms in Banach spaces. We also give an application to generalized set-valued implicit variational inequalities in real Hilbert spaces.

Controllability for an Infinite-Time Horizon of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions

In this paper, we establish sufficient conditions for the controllability on semi-infinite intervals of second-order differential inclusions in Banach spaces with nonlocal conditions. We rely on a fixed-point theorem due to Ma, which is an extension to multivalued maps of the Schaefer theorem on locally convex topological spaces.

On some classes of operator inclusions with lower semicontinuous nonlinearities

We consider a class of multimaps which are the composition of a superposition multioperator ${\mathcal P}_F$ generated by a nonconvex-valued almost lower semicontinuous nonlinearity $F$ and an abstract solution operator $S$. We prove that under some suitable conditions such multimaps are condensing with respect to a special vector-valued measure of noncompactness and construct a topological degree theory for this class of multimaps yielding some fixed point principles. It is shown how abstract results can be applied to semilinear inclusions, inclusions with $m$-accretive operators and time-dependent subdifferentials, nonlinear evolution inclusions and integral inclusions in Banach spaces.

Mixed type semicontinuous differential inclusions in Banach spaces

We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with tim

On second order boundary value problems for functional differential inclusions in Banach spaces

We investigate the existence of solutions on a compact interval to second order boundary value problems for a class of functional differential inclusions in Banach spaces. We rely on a fixed point theorem for condensing maps due to Martelli.

Hyperbolic functional differential inclusions in Banach spaces with nonlocal conditions

In this paper we investigate the existence of solutions to an hyperbolic functional differential inclusion in Banach spaces with nonlocal conditions. We shall rely on a. fixed point theorem for condensing maps due to of Martelli.

A Tikhonov type Theorem for abstract parabolic differential inclusions in Banach spaces

We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for e ≥ 0, where e is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset ZL(e) of the solution set of the singularly perturbed system. This subset is the set of the Holder continuous solutions defined in [0, d], d > 0 †Research supported by the project “Qualitative analysis and control of dynamical systems” at the University of Siena and FRBR grant 99-01-00333. 208 A. Gudovich, M. Kamenski and P. Nistri with prescribed exponent and constant L. We show that ZL(e) is uppersemicontinuous at e = 0 in the C[0, d]× C[δ, d] topology for any δ ∈ (0, d].

Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Existence Results on Infinite Intervals for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

Abstract In this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem.

Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions

In this paper, we establish sufficient conditions for the controllability ofsecond-order differential inclusions in Banach spaces with nonlocalconditions. We rely on a fixed-point theorem for condensing maps due toMartelli.

Set-Valued Variational Inclusions in Banach Spaces

The purpose of this paper is to introduce and study a class of set-valued variational inclusions without compactness condition in Banach spaces. By using Michael's selection theorem and Nadler's theorem, an existence theorem and an iterative algorithm for solving this kind of set-valued variational inclusions in Banach spaces are established and suggested.

An Existence Result on Noncompact Intervals for Second Order Functional Differential Inclusions

In this paper we investigate the existence of mild solutions on an infinite interval for second order functional differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.

An Existence Result for Second Order Functional Differential Inclusions

In this paper we investigate the existence of mild solutions on a compact interval for second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem for condensing maps due to Martelli.

Generalized Set-Valued Variational Inclusions in Banach Spaces

In this paper, a generalization and improvement of Noor's theorem for generalized set-valued variational inclusion in real Banach spaces is studied. The results presented in this paper generalize, improve, and unify a number of recent results.

Fixed Point Theorems for Set-Valued Maps and Existence Principles for Integral Inclusions

New fixed point theorems of Mönch type are presented for set-valued maps. These theorems are then used to establish general existence principles for Hammerstein integral inclusions in Banach spaces.

A result on the singular perturbation theory for differential inclusions in Banach spaces

We provide conditions which ensure that the solution set of the Cauchy problem for a singularly perturbed system of differential inclusions in infinite dimensional Banach spaces is upper semicontinuous with respect to the parameter $\varepsilon\ge0$ of the perturbation. The main tools are represented by suitable introduced measures of noncompactness and the topological degree theory in locally convex spaces.

On a controllability problem for systems governed by semilinear functional differential inclusions in Banach spaces

For a Banach space $E$, a given pair $(\overline p, \overline x)\in[0,a]\times E$, and control system governed by a semilinear functional differential includion of the form $$ x' (t)\in Ax(t) +F(t, x(t), Tx) $$ the existence of a mild trajectory of $x(t)$ satisfying the condition $x(\overline p)=\overline x$ is considered. Using topological methods we develop an unified approach to the cases when a multivalued nonlinearity $F$ is Caratheodory upper semicontinuous or almost lower semicontinuous and an abstract extension operator $T$ allows to deal with variable and infinite delay. For the Caratheodory case, the compactness of the solutions set and, as a corollary, an optimization result are obtained.