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Research Article | Open Access

Variational approach for a Steklov problem involving nonstandard growth conditions

Dicle University, Faculty of Science, Department of Mathematics, 21280-Diyarbakir, Turkey
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Abstract

The aim of this paper is to study the multiplicity of solutions for a nonlocal p ( x )-Kirchhoff type problem with Steklov boundary value in variable exponent Sobolev spaces. We prove the existence of at least three solutions and a nontrivial weak solution of the problem, using the Ricceri's three critical points theorem together with Mountain Pass theorem.

Keywords

variational methodsp(x)-Kirchhoff type equationSteklov boundary valueRicceri's critical points theoremweak solution
CLC number: 35J60, 47J30, 35A15

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 5352-5368
DOI: 10.3934/math.2023269

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Cite this article:
Yucedag Z. Variational approach for a Steklov problem involving nonstandard growth conditions. AIMS Mathematics, 2023, 8(3): 5352-5368. https://doi.org/10.3934/math.2023269

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Received: 27 June 2022
Revised: 27 November 2022
Accepted: 01 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

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