Multiple positive solutions for a Schrödinger-Poisson system with critical and supercritical growths

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9244e

Jun Lei, Hong-Min Suo

引用次数: 0

Abstract

In this paper, we are concerned with the following Schrödinger-Poisson system $$ \begin{cases} -\Delta u+u+\lambda\phi u= Q(x)|u|^{4}u+\mu \dfrac{|x|^\beta}{1+|x|^\beta}|u|^{q-2}u&in \mathbb{R}^3, -\Delta \phi=u^{2} &in \mathbb{R}^3, \end{cases} $$ where $0< \beta<3$, $60$ are real parameters. By the variational method and the Nehari method, we obtain that the system has $k$ positive solutions.

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临界和超临界生长Schrödinger-Poisson系统的多个正解

本文研究如下Schrödinger-Poisson系统$$ \begin{cases} -\Delta u+u+\lambda\phi u= Q(x)|u|^{4}u+\mu \dfrac{|x|^\beta}{1+|x|^\beta}|u|^{q-2}u&in \mathbb{R}^3, -\Delta \phi=u^{2} &in \mathbb{R}^3, \end{cases} $$，其中$0< \beta<3$, $6<q<6+2\beta$, $Q(x)$是$\mathbb{R}^3$上的正连续函数，$\lambda,\mu>0$是实参数。通过变分法和Nehari法，得到了系统有$k$正解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.