M. Mosa Al-Shomrani, M. Ben Mohamed Salah, A. Ghanmi, K. Kefi, “Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents”, Mat. Zametki, 2021, Volume 110, Issue 6,Pages <nobr>830

This article is cited in 2 papers

Papers published in the English version of the journal

Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents

M. Mosa Al-Shomrani^a, M. Ben Mohamed Salah^b, A. Ghanmi^b, K. Kefi^c

^a Department of Mathematics, Faculty of Science, King Abdulaziz university, P. O. Box 80203, Jeddah, 21589 Saudi Arabia
^b Mathematics Department, Faculty of Sciences, University of Tunis El Manar, Tunis, 2092 Tunisia
^c Faculty of Computer Science and Information Technology, Northern Border University, Rafha, 9111 Saudi Arabia

Abstract: This paper deals with the existence of a solution of a problem involving Leray–Lions type operators in Sobolev spaces with variable exponent. The proofs of our main results combine variational methods with energy estimates and Ekeland's variational principle. This paper improves and generalizes previous ones in literature, more precisely those of K. Kefi and V. Rãdulescu (Z. Angew. Math. Phys. 68, 80 (2017)) and M. M Boureanu (Discrete Contin. Dyn. Syst. Ser S, 12 (2) : 231-243 (2019)).

Keywords: Leray–Lions type operators, variational methods, generalized Sobolev space, fourth-order partial differential equations, variable exponents, Ekeland's variational principle.

Received: 17.11.2020
Revised: 20.06.2021

Language: English