Abstract:In this paper, we consider the quasilinear Schrödinger-Poisson system with concave and convex nonlinearities
\begin{align*}
\begin{cases}
-\Delta_{p} u+\lambda V(x)|u|^{p-2}u + \mu \phi |u|^{p-2}u= a(x)|u|^{m-2}u + b(x)|u|^{q-2}u & \ \ \ \mathrm{in}\ \mathbb{R}^{3},
-\Delta \phi=|u|^{p} &\ \ \ \mathrm{in}\ \mathbb{R}^{3},
\end{cases}
\end{align*}
where $\lambda >0, ~\mu >0$, $\frac{3}{2}<p<3$, $1< q<p < m < 2p$
and $\Delta_{p} u= \hbox{div}(|\nabla u|^{p-2}\nabla u)$. We assume that $V(x) \in C(\mathbb{R}^{3}, \mathbb{R})$ is a steep potential well, while $a(x)$ and $b(x)$ are allowed to be sign-changing and satisfy some suitable assumptions in $\mathbb{R}^3$. By using the Ekeland's variational principle and combining the constraint approach, we prove that the system admits two positive solutions.
From: Lanxin Huang [view email]
[v1]
Wed, 17 Jun 2026 13:45:41 UTC (23 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。