International Journal of Nonlinear Analysis and Applications
A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces
Document Type : Research Paper
Authors
1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Abstract
In this article, we introduce the notion of $(\alpha,\beta)$-generalized Meir-Keeler condensing operator in a Banach space, a characterization using strictly L-functions and provide an extension of Darbo's fixed point theorem associated with measures of noncompactness. Then, we establish some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. As an application, we study the problem of existence of entire solutions for a general system of nonlinear integral-differential equations in a Sobolev space. Further, an example is presented to verify the effectiveness and applicability of our main results.
Keywords
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