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K.Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.

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Article

The Solutions of Initial Value Problems for Second-order Integro-differential Equations with Delayed Arguments in Banach Spaces

1School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, P. R. China


Turkish Journal of Analysis and Number Theory. 2015, Vol. 3 No. 6, 154-159
DOI: 10.12691/tjant-3-6-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Tingting Guan. The Solutions of Initial Value Problems for Second-order Integro-differential Equations with Delayed Arguments in Banach Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(6):154-159. doi: 10.12691/tjant-3-6-3.

Correspondence to: Tingting  Guan, School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, P. R. China. Email: guantingting1985@163.com

Abstract

By using the partial order method and some new comparison results, the maximal or minimal solution of the initial value problem for nonlinear second order integro-differential equations with delayed arguments in Banach spaces are investigated. In this paper, we require only a lower solution or an upper solution and some weaker conditions presented here, and we extend and improve some recent results (see [1-11]).

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