带 $p$-拉普拉斯算子的非线性薛定谔-泊松系统的无穷多变号解
偏微分方程分析
2022-12-07 v1
摘要
本文考虑如下带 -拉普拉斯算子的薛定谔-泊松系统 \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} 我们研究多个变号解的存在性。利用下降流不变集方法，我们证明该系统有无穷多变号解。该系统是由 -拉普拉斯薛定谔方程与泊松方程耦合的新系统。我们的结果补充了 Zhaoli Liu、Zhiqiang Wang、Jianjun Zhang（Annali di Matematica Pura ed Applicata, 195(3):775-794(2016)）的研究。
关键词
引用
@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}
}
备注
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