Functional Evolution Inclusions Research Articles

Periodic Mild Solutions of Infinite Delay not Instantaneous Impulsive Evolution Inclusions

This paper deals with the existence of periodic mild solutions for a class of functional evolution inclusions. We use a multivalued fixed point theorem in Banach spaces combined with the technique of measure of noncompactness. We show that the Poincare operator is a condensing operator with respect to Kuratowski’s measure of noncompactness in a determined phase space, and then derive periodic solutions from bounded solutions by using Sadovskii’s fixed point theorem.

Topological properties of C^{0}-solution set for impulsive evolution inclusions

In this paper, we study the topological properties to a C^{0}-solution set of impulsive evolution inclusions. The definition of C^{0}-solutions for impulsive functional evolution inclusions is introduced. The R_{delta}-property of C^{0}-solution set is studied for compact as well as noncompact semigroups on compact intervals. Applying the inverse limit method, the R_{delta}-structure on noncompact intervals is obtained.

Topological properties of solution sets for partial functional evolution inclusions

This paper deals with functional evolution inclusions of neutral type in Banach space when the semigroup is compact as well as noncompact. The topological properties of the solution set is investigated. It is shown that the solution set is nonempty, compact and an Rδ-set which means that the solution set may not be a singleton but, from the point of view of algebraic topology, it is equivalent to a point, in the sense that it has the same homology group as one-point space. As a sample of application, we consider a partial differential inclusion at end of the paper.

Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces

Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces

On the dynamics generated by a class of functional evolution inclusions

The long-time behavior for a class of nonlinear functional evolution inclusions involving accretive operators is studied. We prove the existence of a compact global attractor by using the condensivity of the translation operator along the trajectories of our system.

Cauchy problems for functional evolution inclusions involving accretive operators

We study the existence and stability of solutions for a class of nonlinear functional evolution inclusions involving accretive operators. Our approach is employing the xed point theory for multivalued maps and using estimates via the Hausdor measure of noncompactness.

On Nonconvex functional evolution inclusions involving m-dissipative operators

On Nonconvex functional evolution inclusions involving m-dissipative operators