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

Huiting He; Mohamed Ousbika; Zakaria El Allali; Jiabin Zuo; Huiting He; Mohamed Ousbika; Zakaria El Allali; Jiabin Zuo

doi:10.3934/cam.2023030

Communications in Analysis and Mechanics

2023, Volume 15, Issue 4: 598-610. doi: 10.3934/cam.2023030

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

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P. R. China
2.
University Mohammed first Oujda, Faculty multidisciplinary of Nador, Oriental applied mathematics laboratory, Team of Modeling and Scientific Computing, Morocco

Received: 24 July 2023 Revised: 25 September 2023 Accepted: 26 September 2023 Published: 10 October 2023
39A10, 34B15, 35B38

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 $ \lambda $ 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.
- partial discrete nonlinear problem,
- critical point theory,
- $ p $-Laplacian,
- non-trivial solutions
Citation: Huiting He, Mohamed Ousbika, Zakaria El Allali, Jiabin Zuo. Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with $ p $-Laplacian[J]. Communications in Analysis and Mechanics, 2023, 15(4): 598-610. doi: 10.3934/cam.2023030

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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 $ \lambda $ 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.

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