Research Article

Multiplicity of positive solution for Schrödinger-Poisson system with p-Laplacian

Published in: Quaestiones Mathematicae
Volume 46 , issue 10 , 2023 , pages: 2203–2232

DOI: 10.2989/16073606.2022.2142690

Author(s): Weiqiang Zhang Lanzhou University, People’s Republic of China , Peihao Zhao Lanzhou University, People’s Republic of China

Keywords: Primary: 35B09 , 35J62 , 35J92 , Schrödinger-Poisson system , p-Laplacian , variational methods , Ljusternik-Schnirelmann theory

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Abstract

In this paper, we consider the positive solutions for a Schrödinger-Poisson system containing p-Laplacian and Poisson equation. With a local condition on the potential, by using penalization method, Nehari manifold and Ljusternik-Schnirelmann category theory, the multiplicity and concentration of solutions are obtained.

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