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Research Article | Open Access

Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian

Huiting He1, Mohamed Ousbika2, Zakaria El Allali2, Jiabin Zuo1( )
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P. R. China
University Mohammed first Oujda, Faculty multidisciplinary of Nador, Oriental applied mathematics laboratory, Team of Modeling and Scientific Computing, Morocco
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Abstract

We investigate the non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian by applying Ricceri's variational principle and a two non-zero critical points theorem. In addition, we identify open intervals of the parameter λ under appropriate constraints imposed on the nonlinear term. This allows us to ensure that the nonlinear problem has at least one or two non-trivial solutions.

Keywords

partial discrete nonlinear problemcritical point theoryp-Laplaciannon-trivial solutions
CLC number: 39A10, 34B15, 35B38

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Communications in Analysis and Mechanics
Volume 15 Issue 4,
November 2023
Pages 598-610
DOI: 10.3934/cam.2023030

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Cite this article:
He H, Ousbika M, El Allali Z, et al. Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian. Communications in Analysis and Mechanics, 2023, 15(4): 598-610. https://doi.org/10.3934/cam.2023030

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Received: 24 July 2023
Revised: 25 September 2023
Accepted: 26 September 2023
Published: 10 October 2023
©2023 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)