Journal of Advances in Mathematics and Computer Science

Existence of Coupled Quasi-solutions of Nonlinear Integro-Differential Equations of Volterra Type in Banach Spaces

Yan Liang *

Zhengzhou Infant Normal College, Zhengzhou 450000, China.

*Author to whom correspondence should be addressed.

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Abstract

We study an initial value problem for a class of integro-differential equations of Volterra type in a real Banach space. Using method of upper and lower solutions and M¨onch and Von Harten theorem, we obtain an existence theorem of coupled quasi-solutions, which is an extension of those established by Y. Chen and W. Zhuang in [1].

Keywords: Banach space, measure of noncompactness, lower and upper solutions, normal cone, Quasi-solution

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