Abstract

This article is concerned with the existence of almost automorphic mild solutions to second order evolution equations of the form where A generates a strongly continuous semigroup and f is an almost automorphic function. Using the notion of uniform spectrum of a function and the method of sums of commuting operators in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to (*) in terms of spectrum of A and uniform spectrum of f. Moreover, we study the nonlinear perturbation of this equation and obtain an extension of results by Diagana and N’Guérékata.