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

Al-Shomrani Mosa, Salah Ben Mohamed, A Ghanmi and K Kefi
Mathematical notes (Rossiĭskaia akademiia nauk), Vol.110(5-6), pp.830-841
01/11/2021
DOI: https://doi.org/10.1134/S0001434621110201

Abstract

Elliptic functions Operators Sobolev space Variational methods
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)).

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