Variational approach for a Steklov problem involving nonstandard growth conditions

Zehra Yucedag; Zehra Yucedag

doi:10.3934/math.2023269

AIMS Mathematics

2023, Volume 8, Issue 3: 5352-5368. doi: 10.3934/math.2023269

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Variational approach for a Steklov problem involving nonstandard growth conditions

Zehra Yucedag ^,

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

Received: 27 June 2022 Revised: 27 November 2022 Accepted: 01 December 2022 Published: 15 December 2022
MSC : 35J60, 47J30, 35A15

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.
- variational methods,
- $ p(x) $-Kirchhoff type equation,
- Steklov boundary value,
- Ricceri's critical points theorem,
- weak solution
Citation: Zehra Yucedag. Variational approach for a Steklov problem involving nonstandard growth conditions[J]. AIMS Mathematics, 2023, 8(3): 5352-5368. doi: 10.3934/math.2023269

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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.

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