Infinitely many sign-changing solutions for the nonlinear Schr\"odinger-Poisson system with $p$-Laplacian
Abstract
In this paper, we consider the following Schr\"odinger-Poisson system with -laplacian \begin{equation} \begin{cases} -\Delta_{p}u+V(x)|u|^{p-2}u+\phi|u|^{p-2}u=f(u)\qquad&x\in\mathbb{R}^{3},\newline -\Delta\phi=|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 Schr\"odinger equation of -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)).
Keywords
Cite
@article{arxiv.2212.03138,
title = {Infinitely many sign-changing solutions for the nonlinear Schr\"odinger-Poisson system with $p$-Laplacian},
author = {Shuo Ren and Huixing Zhang and Zhen Cheng and Yan Gao},
journal= {arXiv preprint arXiv:2212.03138},
year = {2022}
}
Comments
33 pages. arXiv admin note: substantial text overlap with arXiv:1408.6870 by other authors; text overlap with arXiv:1812.09240, arXiv:1811.05881 by other authors