Almost periodic solutions of semilinear equations with analytic semigroups in Banach spaces

Abstract

We establish the existence and uniqueness of almost periodic solutions of a class of semilinear equations having analytic semigroups. Our basic tool in this paper is the use of fractional powers of operators.

Keywords

• Semilinear equation in Banach spaces
• almost periodic solution
• infinitesimal generator of analytic semigroups
• fractional powers.