Multiple solutions for nonlocal elliptic problems driven by $ p(x) $-biharmonic operator

Fang-Fang Liao; Shapour Heidarkhani; Shahin Moradi; Fang-Fang Liao; Shapour Heidarkhani; Shahin Moradi

doi:10.3934/math.2021246

AIMS Mathematics

2021, Volume 6, Issue 4: 4156-4172. doi: 10.3934/math.2021246

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Research article

Multiple solutions for nonlocal elliptic problems driven by $ p(x) $-biharmonic operator

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2.
Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran

Received: 07 October 2020 Accepted: 25 January 2021 Published: 05 February 2021
MSC : 35J20, 35J60, 47J30

In this article, we study the existence of at least three distinct weak solutions for nonlocal elliptic problems involving $ p(x) $-biharmonic operator. The results are obtained by means of variational methods. We also provide an example in order to illustrate our main abstract results. We extend and improve some recent results.
- $ p(x) $-biharmonic operator,
- nonlocal elliptic problem,
- three solutions,
- variational methods
Citation: Fang-Fang Liao, Shapour Heidarkhani, Shahin Moradi. Multiple solutions for nonlocal elliptic problems driven by $ p(x) $-biharmonic operator[J]. AIMS Mathematics, 2021, 6(4): 4156-4172. doi: 10.3934/math.2021246

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Abstract

In this article, we study the existence of at least three distinct weak solutions for nonlocal elliptic problems involving $ p(x) $-biharmonic operator. The results are obtained by means of variational methods. We also provide an example in order to illustrate our main abstract results. We extend and improve some recent results.

References

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