Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces

摘要

In this paper we prove some existence and uniqueness results for pseudo almost automorphic and weighted pseudo almost automorphic solutions to a class of semi-linear differential equations in Hilbert spaces. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and the method of the invariant subspaces for unbounded linear operators. Moreover, an application is also given to illustrate our main results.