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arXiv · 2212.03138

Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with $p$-Laplacian

Shuo Ren·Huixing Zhang·Zhen Cheng·Yan Gao
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Abstract

In this paper, we consider the following Schrödinger-Poisson system with $p$-laplacian \begin{equation} \begin{cases} -Δ_{p}u+V(x)|u|^{p-2}u+ϕ|u|^{p-2}u=f(u)\qquad&x\in\mathbb{R}^{3},\newline -Δϕ=|u|^{p}&x\in\mathbb{R}^{3}. \end{cases}\notag \end{equation} We investigate the existence of multiple sign-changing solutions. By using the method of invariant sets of descending flow, we prove that this system has infinitely many sign-changing solutions. This system is new one coupled by Schrödinger equation of $p$-laplacian with a Poisson equation. Our results complement the study made by Zhaoli Liu, Zhiqiang Wang, Jianjun Zhang (Annali di Matematica Pura ed Applicata, 195(3):775-794(2016)).

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Shuo Ren, Huixing Zhang, Zhen Cheng, Yan Gao. 2022-12-06. Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with $p$-Laplacian. https://arxiv.org/abs/2212.03138

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