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
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
收藏
页数:26
相关论文
共 35 条
[21]   Ground states for Kirchhoff equations without compact condition [J].
Guo, Zuji .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (07) :2884-2902
[22]   Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3 [J].
He, Xiaoming ;
Zou, Wenming .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (02) :1813-1834
[23]   The role played by space dimension in elliptic critical problems [J].
Jannelli, E .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) :407-426
[24]   A positive solution for a nonlinear Schrodinger equation on RN [J].
Jeanjean, L ;
Tanaka, K .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2005, 54 (02) :443-464
[25]   A remark on least energy solutions in RN [J].
Jeanjean, L ;
Tanaka, K .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (08) :2399-2408
[26]  
Kirchhoff G., 1883, MECHANIK
[27]   ELECTRON CAPTURE BY POLAR MOLECULES [J].
LEVYLEBL.JM .
PHYSICAL REVIEW, 1967, 153 (01) :1-&
[28]   Existence and asymptotic behavior of ground state solutions for Schrodinger equations with Hardy potential and Berestycki-Lions type conditions [J].
Li, Gui-Dong ;
Li, Yong-Yong ;
Tang, Chun-Lei .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 275 :77-115
[29]   Remarks on an elliptic equation of Kirchhoff type [J].
Ma, T. F. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) :E1967-E1977
[30]   Nontrivial solutions of Kirchhoff-type problems via the Yang index [J].
Perera, K ;
Zhang, ZT .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (01) :246-255