Electron. J. Differential Equations, Vol. 2022 (2022), No. 81, pp. 1-17.

Mixed local and nonlocal Schrodinger-Poisson type system involving variable exponents

Xiaolu Lin, Shenzhou Zheng

Abstract:
We consider the existence of solutions for a class of Schrodinger-Poisson type equations with mixed local and nonlocal p-Laplacian. More precisely, we obtain two distinct nontrivial solutions for the problem involving variable exponents growth by the variational methods. Moreover, the phenomena of concentration and multiplicity of solutions are also investigated as λ→∞.

Submitted May 4, 2022. Published November 28, 2022.
Math Subject Classifications: 35A15, 35B33, 35R11.
Key Words: Mixed local and nonlocal operator; Schrodinger-Poisson type system; multiple solutions; asymptotic behavior; symmetric mountain pass lemma.
DOI: https://doi.org/10.58997/ejde.2022.81

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Xiaolu Lin
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: 19118003@bjtu.edu.cn
Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn

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