In order to obtain the existence of an almost periodic functional difference equation xðn þ 1Þ ¼ f ðn; x n Þ; n [ Z þ and where x n is defined by x n ðsÞ ¼ xðn þ sÞ for s [ Z 2 ; on an axiomatic phase space B, we consider a certain stability property, which is referred to as BS-stable under disturbances from V( f ) with respect to K, this stability implies r-stable under disturbances from V( f ) with respect to compact set K.
SynopsisWe consider a system of integrodifferential equationswhere f(t, x) and F(t, s, x, y) are almost periodic in t uniformly for parameters, and we assume that the system has a bounded solution u(t). To discuss the existence of an almost periodic solution, we consider the relationship between the total stability of u(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 an n-species system.
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