Differential Inclusions In Banach Spaces Research Articles

Existence of solutions to differential inclusions in Banach spaces

In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces. First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end, the existence theorem of solutions to differential inclusions is obtained.

Extreme Continuous Selectors of Multivalued Maps and Their Applications

A theorem on the existence of continuous selectors whose values are extreme points is proved for a class of multivalued maps. The theorem is used to study existence and properties of solutions to differential inclusions in Banach spaces.

Periodic solutions and optimization problems for a class of semilinear parabolic control systems

This paper is devoted to the study of the existence of periodic solutions for a class of control problems described by a semilinear parabolic equation. Related optimization problems are also considered. Periodic control problems and optimal periodic control problems for evolution equations described both by ordinary differential equations and by parabolic equations arise in many different situations. Examples are found in the theory of chemical processes [7], biomedical models [13], competing species ([6], and the extensive references therein), thermostat problems [3], [5], [18] and [20] (and the references therein). Several authors have also treated the existence of periodic solutions of differential inclusions in Banach spaces. These differential inclusions can model periodic control problems. In fact, under suitable assumptions, a large class of control problems can be reduced to the problem of finding solutions of a differential inclusion. We mention here the following papers: [8], [9], [10], [15], [16] and the references therein. The variety of techniques used in the quoted papers is quite large. Referring only to those papers dealing with parabolic equations, we recall that in [6] the properties of the Poincare map and the theory of ordered spaces

Fixed points and coupled fixed points for increasing operators with applications to differential inclusions in Banach spaces

Under some general continuous and compact conditions, the existence problems of fixed points and coupled fixed points for increasing operators are studied. As an application, we utilize the results obtained to study the existence of solutions for differential inclusions in Banach spaces.

Lower semi-continuous nonconvex perturbation of m-accrative differential inclusions in Banach spaces

In this paper we prove the existence of solutions of the differential inclusions $$\left\{ \begin{gathered} \dot X(t) \in - A_t (X(t)) + F(t,X(t)),,0 \leqslant t \leqslant T_0 \hfill \\ X(0) = x_0 \hfill \\ \end{gathered} \right.$$ whereAt is a multivaluedm-accretive operator on a Banach spaceE andF is a measurable multifunction defined on the set\(G = \overline {\{ (t,x):A_t (x) \ne 0/\} } \), lower semicontinuous inx and its values are not necessarily convex inE. This result generalizes some results in [1] and [9].

Classical solutions of partial differential inclusions in banach spaces

In this paper we deal with classical solutions of the problem in a Banach space. In particular, we prove that the set all classical solutions of the above problem is a retract of an appropriate function space

Non-convex-valued differential inclusions in Banach spaces

Non-convex-valued differential inclusions in Banach spaces

On bounded solutions of differential inclusions in Banach spaces

Let X be a separable Banach space and t ϵ R +. We prove the existence and an asymptotic property of bounded solutions of the differential inclusion x ̇ (t) ϵ A(t)x(t) + F(t, x(t)) . The orientor field F(·,·) satisfies Carathéodory-type conditions and a regularity condition in terms of the Hausdorff measure of noncompactness β(·). In the process of proving our main theorem we also obtain some new results about measurable multifunctions of independent interest.

A property of the solution set of differential inclusions in banach spaces with a caratheodory orientor field

We examine the solution set of differential inclusions in separable Banach spaces with a Caratheodory orientor field i.e. teF(t ,x) is measurable and xeF(t,x) is completely u.s.c. We show that the solution set is an Rδ set in C(T,X), extending this way earlier results by Lasry-Robert, Himmelberg-Van Vleck, De Blasi - Myjak and Papageorgiou

On Multivalued Evolution Equations and Differential Inclusions in Banach Spaces

On Multivalued Evolution Equations and Differential Inclusions in Banach Spaces

Differential inclusions in Banach spaces

Differential inclusions in Banach spaces

A relaxation theorem for differential inclusions in Banach spaces

A relaxation theorem for differential inclusions in Banach spaces

Random differential inclusions in Banach spaces

Random differential inclusions in Banach spaces

A stability result for differential inclusions in Banach spaces

On etablit un resultat de stabilite pour les inclusions differentielles definies sur un espace de Banach separable