No abstract

No abstract

This work aims to study the existence and uniqueness of pseudo compact almost automorphic solution for some dissipative ordinary and functional differential equations. We prove the existence and uniqueness of pseudo compact almost automorphic solution for dissipative differential equations in Banach spaces and then we apply this result to show the existence of pseudo compact almost automorphic solutions for some functional differential equations.

In this article, we prove a number of properties concerning a (new) class of (Stepanov-like) Eberlein-weakly almost periodic (S P -E.w. a. p.) functions with values in a Banach space. We use the results obtained to study the asymptotic behaviour of solutions to the evolution equation:where A is the generator of an integral resolvent family in a Banach space X, a 2 L 1 (R), and f is a given X-valued function on R. The objective is to deduce Eberlein-weakly almost periodicity (in Stepanov-like sense) of the solution u from corresponding properties on the part f.

No abstract