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)).
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Acknowledgments
The first author acknowledges with thanks the support of the Deanship Scientific Research (DSR) at King Abdulaziz University, Jeddah.
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Al-Shomrani, M.M., Salah, M.B.M., Ghanmi, A. et al. Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents. Math Notes 110, 830–841 (2021). https://doi.org/10.1134/S0001434621110201
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DOI: https://doi.org/10.1134/S0001434621110201