Electron. J. Differential Equations, Vol. 2023 (2023), No. 28, pp. 1-14.

Multiple solutions for nonhomogeneous Schrodinger-Poisson system with p-Laplacian

Lanxin Huang, Jiabao Su

Abstract:
This article concerns the existence of solutions to the Schrodinger-Poisson system $$\displaylines{ -\Delta_p u+|u|^{p-2}u+\lambda\phi u=|u|^{q-2}u+h(x) \quad \hbox{in }\mathbb{R}^3,\\ -\Delta \phi=u^2 \quad \hbox{in }\mathbb{R}^3, }$$ where \( 4/3 < p < 12/5 \), \( p < q < p^{*}=3p/(3-p) \), \(\Delta_p u =\hbox{div}(|\nabla u|^{p-2}\nabla u)\), \(\lambda >0\), and \(h \not= 0\). The multiplicity results are obtained by using Ekeland's variational principle and the mountain pass theorem.

Submitted July 8, 2022. Published March 11, 2023.
Math Subject Classifications: 35J10, 35J50, 35J60, 35J92.
Key Words: Nonhomogeneous Schrodinger-Poisson system; variational methods; multiple solutions; p-Laplacian.
DOI: https://doi.org/10.58997/ejde.2023.28

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Lanxin Huang
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: 812419761@qq.com
Jiabao Su
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: sujb@cnu.edu.cn

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