Existence of Ground State Solutions for Kirchhoff Problems with Hardy Potential

被引：0

作者：

Zhou, MengYun ^{[1
]}

Lan, YongYi ^{[1
]}

机构：

[1] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2023年 / 22卷 / 04期

关键词：

Kirchhoff problems; Berestycki-Lions type conditions; Hardy potential; Pohozaev identity; Ground state solution; POSITIVE SOLUTIONS; ELLIPTIC EQUATION; ASYMPTOTIC-BEHAVIOR; CRITICAL EXPONENTS; HEAT-EQUATION; MULTIPLICITY;

D O I：

10.1007/s12346-023-00841-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study is concerned with the following Kirchhoff problem: -(a + b integral(R3) vertical bar del u vertical bar(2)dx) Delta u - mu/vertical bar x vertical bar(2)u = g(u) in R-3\{0}, (A) where a, b > 0 are constants, mu < 1/4. 1/vertical bar x vertical bar(2) is called the Hardy potential and g : R -> R is a continuous function that satisfies the Berestycki-Lion type condition. Using variational methods, we establish two existence results for problem (A) under different conditions for g. Furthermore, if mu < 0, we prove that the mountain pass level in H-1(R-3) can not be achieved.

引用

页数：26

共 35 条

[1] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].