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

Wasfi Shatanawi¹  Taqi A.M. Shatnawi²  Noura Laksaci³  Ahmed Boudaoui³ 

[1] Prince Sultan University;The Hashemite University;University of Adrar;

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

DOI  :  10.15388/namc.2022.27.27961

来源: DOAJ

【 摘 要 】

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].

【 授权许可】

Unknown