ABSTRACT

In this paper, we study the existence of compactly supported solutions for the Schrödinger equations with indefinite potentials $-{\mathrm{\Delta }}_{p}u+V\left(x\right)u=a\left(x\right)|u{|}^{q-1}u,x\in {\mathbb{R}}^N,$ where $N\ge 2$, 1<p<2, 0<q<p−1, and $a\left(x\right),V\left(x\right)$ change sign in ${\mathbb{R}}^N$. Firstly, we establish the existence of infinitely many weak solution. Next, we study the compactness of support of classical solutions for the above equation. This paper is a continuation of the recent work established by [Bedoui N, Ounaies H. Qualitative properties and support compactness of solutions for quasilinear Schrödinger equation with sign changing potentials. Nonlinear Anal. 2020;198:111843.].

摘要

在本文中，我们研究了具有不定势的薛定谔方程的紧支撑解的存在性$-{\mathrm{\Delta }}_p你+五\left(X\right)你=\mathrm{一个}\left(X\right)|你{|}^{q-1}你,X\in {\mathbb{R}}^{ñ},$在哪里$ñ\ge 2$, 1< p <2, 0< q < p -1, 和$\mathrm{一个}\left(X\right),五\left(X\right)$更改登录${\mathbb{R}}^{ñ}$. 首先，我们建立了无限多弱解的存在性。接下来，我们研究上述方程经典解的支持紧度。本文是 [Bedoui N, Ounaies H. 定性性质和支持具有符号变化势的拟线性薛定谔方程解的紧致性的最近工作的延续。非线性肛门。2020；198:111843。]。