Existence results of nontrivial solutions for a new $ p(x) $-biharmonic problem with weight function

Wei Guo; Jinfu Yang; Jiafeng Zhang; Wei Guo; Jinfu Yang; Jiafeng Zhang

doi:10.3934/math.2022473

AIMS Mathematics

2022, Volume 7, Issue 5: 8491-8509. doi: 10.3934/math.2022473

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Research article

Existence results of nontrivial solutions for a new $ p(x) $-biharmonic problem with weight function

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Received: 25 October 2021 Revised: 26 January 2022 Accepted: 07 February 2022 Published: 28 February 2022
MSC : 35D05, 47J20, 35J50

In this paper, we study a class of $ p(x) $-biharmonic problems with negative nonlocal terms and weight function. Using the mountain pass theorem and the Ekeland's variational principle, at least three solutions are obtained. We also give some comments on the existence of infinite many solutions for our problem when the nonlinear term is a general function.
- nontrivial solutions,
- $ p(x) $-biharmonic problem,
- mountain pass theorem,
- Ekeland's variational principle,
- variable exponent
Citation: Wei Guo, Jinfu Yang, Jiafeng Zhang. Existence results of nontrivial solutions for a new $ p(x) $-biharmonic problem with weight function[J]. AIMS Mathematics, 2022, 7(5): 8491-8509. doi: 10.3934/math.2022473

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Abstract

In this paper, we study a class of $ p(x) $-biharmonic problems with negative nonlocal terms and weight function. Using the mountain pass theorem and the Ekeland's variational principle, at least three solutions are obtained. We also give some comments on the existence of infinite many solutions for our problem when the nonlinear term is a general function.

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