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Research Article | Open Access

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

Wei Guo, Jinfu Yang, Jiafeng Zhang( )
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
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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.

Keywords

nontrivial solutionsp(x)-biharmonic problemmountain pass theoremEkeland's variational principlevariable exponent
CLC number: 35D05, 47J20, 35J50

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8491-8509
DOI: 10.3934/math.2022473

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Cite this article:
Guo W, Yang J, Zhang J. Existence results of nontrivial solutions for a new p ( x )-biharmonic problem with weight function. AIMS Mathematics, 2022, 7(5): 8491-8509. https://doi.org/10.3934/math.2022473

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Received: 25 October 2021
Revised: 26 January 2022
Accepted: 07 February 2022
Published: 15 May 2022
©2022 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)