Solvability of a system of integral equations in two variables in the weighted Sobolev space W(1,1)-omega(a,b) using a generalized measure of noncompactness
Articles
Taqi A.M. Shatnawi
The Hashemite University
https://orcid.org/0000-0001-5842-3573
Ahmed Boudaoui
University of Adrar
https://orcid.org/0000-0002-4450-7423
Wasfi Shatanawi
Prince Sultan University
https://orcid.org/0000-0001-7492-4933
Noura Laksaci
University of Adrar
https://orcid.org/0000-0001-8773-029X
Published 2022-06-30
https://doi.org/10.15388/namc.2022.27.27961
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Keywords

coupled system of integral equation
weighted Sobolev spaces
Darbo’s fixed point theorem
M-set contractive
generalized measure of noncompactness

How to Cite

Shatnawi T. A., Boudaoui A., Shatanawi W. and Laksaci N. (2022) “Solvability of a system of integral equations in two variables in the weighted Sobolev space W(1,1)-omega(a,b) using a generalized measure of noncompactness”, Nonlinear Analysis: Modelling and Control, 27(5), pp. 927-947. doi: 10.15388/namc.2022.27.27961.

Abstract

In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b). The results were achieved by equipping the space E with the vector-valued norms and using the measure of noncompactness constructed in [F.P. Najafabad, J.J. Nieto, H.A. Kayvanloo, Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations, J. Fixed Point Theory Appl., 22(3), 75, 2020] to applicate the generalized Darbo’s fixed point theorem [J.R. Graef, J. Henderson, and A. Ouahab, Topological Methods for Differential Equations and Inclusions, CRC Press, Boca Raton, FL, 2018].

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