Preservation of stability and asymptotic behaviour of perturbed integrodifferential equations in a Banach space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

Preservation of stability and asymptotic behaviour of perturbed integrodifferential equations in a Banach space

Authors:	B. G. Pachpatte

Affiliation:	(1) Department of Mathematics, Deogiri College, 431004 Aurangabad

Abstract:	In this paper stability and asymptotic behaviour of solutions of the integrodifferential system $x'left( t right) = Aleft( t right)xleft( t right) + fleft( {t,xleft( t right),int_{t_0 }^t {kleft( {t,s,xleft( s right)} right)ds} } right) + gleft( {t,xleft( t right)} right)$ in a Banach space is related to that of the integrodifferential system $y'left( t right) = Aleft( t right)yleft( t right) + fleft( {t,yleft( t right),int_{t_0 }^t {kleft( {t,s,yleft( s right)} right)ds} } right)$ in a Banach space. The results obtained constitute a generalization of similar results for ordinary differential equations in a Banach space, which motivate the approach and proofs.

Keywords:	Integrodifferential equations Banach space stability and asymptotic behaviour asymptotic equivalence
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