Almost periodic solutions in an integrodifferential equation

Abstract

SynopsisWe consider a system of integrodifferential equationswheref(t,x) andF(t,s,x,y) are almost periodic intuniformly for parameters, and we assume that the system has a bounded solutionu(t). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability ofu(t) with respect to a certain metric ρ and the separation condition with respect to ρ. Moreover, we discuss a sufficient condition for the existence of a positive almost periodic solution of a model of the dynamics of ann-species system.