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Research Article | Open Access

On an anisotropic p→(⋅)-Laplace equation with variable singular and sublinear nonlinearities

Faculty of Science and Technology, Applied Mathematics, Athabasca University, AB, Canada
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Abstract

In the present paper, we study an anisotropic p→(⋅)-Laplace equation with combined effects of variable singular and sublinear nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case where the variable singularity β(x) assumes its values in the interval (1,∞).

Keywords

anisotropic singular p(⋅)-Laplacianvariable strong singularityanisotropic variable Sobolev spaceEkeland's variational principle
CLC number: 35A15, 35A21, 35J75, 58E30

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Communications in Analysis and Mechanics
Volume 16 Issue 3,
September 2024
Pages 554-577
DOI: 10.3934/cam.2024026

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Cite this article:
Avci M. On an anisotropic p→(⋅)-Laplace equation with variable singular and sublinear nonlinearities. Communications in Analysis and Mechanics, 2024, 16(3): 554-577. https://doi.org/10.3934/cam.2024026

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Received: 20 February 2024
Revised: 29 July 2024
Accepted: 29 July 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)