New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces

Abstract

In this work we give a new criteria for the existence of periodic and almost periodic solutions for some differential equation in a Banach space. The linear part is nondensely defined and satisfies the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for the existence of periodic and almost periodic solutions for some partial functional differential equation whose linear part is nondensely defined.