论文标题
非线性schrödinger-Poisson系统的许多签字解决方案与$ p $ -laplacian
Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system with $p$-Laplacian
论文作者
论文摘要
在本文中，我们考虑以下具有$ p $ -laplacian \ begin {equation}的schrödinger-Poisson系统 \ begin {case} -Δ_{p} u+v（x）| u |^{p-2} u+ϕ | u |^{p-2} u = f（u）\ qquad＆x \ in \ mathbb {r}^{3} {3}，\ newline -Δϕ = | u |^{p}＆x \ in \ mathbb {r}^{3}。 \ end {case} \ notag \ end {equation}我们研究了多个签名解决方案的存在。通过使用不变的下降流的方法，我们证明该系统具有许多不断变化的解决方案。该系统是由$ p $ laplacian和泊松方程式的Schrödinger方程组合的新系统。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））进行的研究。
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)).
