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Almost periodic solutions in an integrodifferential equation

Published online by Cambridge University Press:  14 November 2011

Y. Hamaya  and
T. Yoshizawa
Y. Hamaya
Affiliation:
Department of Applied Mathematics, Okayama University of Science, Okayama 700, Japan
T. Yoshizawa
Affiliation:
Department of Applied Mathematics, Okayama University of Science, Okayama 700, Japan
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Synopsis

We consider a system of integrodifferential equations

where 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 151 - 159
Copyright
Copyright © Royal Society of Edinburgh 1990

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