Almost automorphic and pseudo-almost automorphic mild solutions to an abstract differential equation in Banach spaces - Zhao, Zhi-Han; Chang, Yong-Kui; Nieto, Juan J. (Nonlinear analysis, 2010)
In this paper we prove some existence results for almost automorphic and pseudo-almost automorphic mild solutions to a class of abstract differential equations in Banach spaces. The main technique is based on some composition theorems combined with the contraction mapping theorem. Finally, we present an application to a semilinear partial differential equation with Dirichlet conditions.