MULTIPLE POSITIVE SOLUTIONS FOR THE SCHRODINGER-POISSON EQUATION WITH CRITICAL GROWTH

被引：4

作者：

Chen, Caixia ^{[1
]}

Qian, Aixia ^{[2
]}

机构：

[1] Jining Univ, Sch Math & Comp Applicat Technol, Jining 273155, Shandong, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

MATHEMATICAL FOUNDATIONS OF COMPUTING | 2022年 / 5卷 / 02期

关键词：

Schrodinger-Poisson equation; Critical exponent; Variational methods; Concentration-compactness principle; Ground state solution; GROUND-STATE SOLUTIONS; EXISTENCE; SYSTEM;

D O I：

10.3934/mfc.2021036

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we consider the following Schrodinger-Poisson equation {-Delta u + u + phi u = u(5) + lambda g(u), in Omega, -Delta phi = u(2), in Omega, u, phi = 0, partial derivative Omega. where Omega is a bounded smooth domain in R-3, lambda > 0 and the nonlinear growth of u(5) reaches the Sobolev critical exponent in three spatial dimensions. With the aid of variational methods and the concentration compactness principle, we prove the problem admits at least two positive solutions and one positive ground state solution.

引用

页码：113 / 128

页数：16

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