Nonlinear integrodifferential equations anda priori bounds on periodic solutions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Nonlinear integrodifferential equations anda priori bounds on periodic solutions

Authors:	T A Burton P W Eloe M N Islam

Institution:	(1) Present address: Department of Mathematics, Southern Illinois University at Carbondale, 62901 Carbondale, Illinois;(2) Present address: Department of Mathematics, University of Dayton, 45469 Dayton, Ohio

Abstract:	Summary This paper studies the existence of aperiodic solution of a nonlinear integrodifferential system of the form $x'(t) = Dx(t) + f\left( {x(t)} \right) + \int\limits_{ - \infty }^t {k(t,s)g\left( {x(s)} \right)ds + p(t)} ,$ , for each continuous periodic function p and under suitable assumptions on f, k and g. A topological transversality method is employed to obtain the existence of periodic solutions. This method relies ona priori bounds on periodic solutions. Several examples are provided where a variant of Liapunov's direct method is employed to obtaina priori bounds on periodic solutions.

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