Singular initial value problem for a system of integro-differential equations unsolved with respect to the derivative

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• 作者：Zden¨§k ?marda ; Yasir Khan
• 关键词：Integro-differential equations ; Topological method of T. Wa?ewski ; Schauder&rsquo ; s fixed point theorem
• 刊名：Applied Mathematics and Computation
• 出版年：2013
• 出版时间：1 October, 2013
• 年：2013
• 卷：222
• 期：Complete
• 页码：290-296
• 全文大小：346 K

文摘

A singular initial value problem for a system of integro-differential equations of the first order unsolved with respect to the derivative of the unknown functions is considered. It is shown that under certain assumptions there is a solution lying in a region, having the vertex coinciding with the initial point, in which the graph of a solution of given singular problem is located. The main result gives asymptotic estimates of a solution and its derivative with respect to a general solution of an auxiliary differential equation. An approach which combines topological method of T. Wa?ewski and Schauder¡¯s fixed point theorem is used. The results generalize some previous ones, where the singular initial value problems for integro-differential equations were studied.