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

Tingting Guan^1,

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

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

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]).

Keywords:
second-order integro-differential equation delayed arguments measure of non-compactness solution monotone iterative technique

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