Ground state solution for the Schrodinger equation with Hardy potential and critical Sobolev exponent

被引：0

作者：

Zhang, Jing ^{[1
]}

Li, Lin ^{[2
,3
]}

机构：

[1] Inner Mongolia Normal Univ, Math Sci Coll, Hohhot 010022, Peoples R China

[2] Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing 400067, Peoples R China

[3] Chongqing Technol & Business Univ, Chongqing Key Lab Social Econ & Appl Stat, Chongqing 400067, Peoples R China

来源：

ASYMPTOTIC ANALYSIS | 2022年 / 129卷 / 3-4期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Schrodinger equation; generalized Nehari manifold; asymptotically periodic; SIGN-CHANGING SOLUTIONS; ELLIPTIC PROBLEMS; EXISTENCE;

D O I：

10.3233/ASY-211737

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following Schrodinger equation {-Delta u - mu u/vertical bar x vertical bar(2) + V(x)u = K(x)vertical bar u vertical bar(2)*(-2)u + f(x, u), x is an element of R-N, u is an element of H-1 (R-N), where N >= 4, 0 <= mu < <(mu)over bar>, (mu) over bar = (N-2)(2)/4, V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

引用

页码：485 / 503

页数：19

共 50 条

[41] Orbital stability of ground states for a Sobolev critical Schrodinger equation
Jeanjean, Louis
Jendrej, Jacek
Le, Thanh Trung
Visciglia, Nicola
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2022, 164 : 158 - 179
[42] On the critical dimension of a semilinear degenerate elliptic equation involving critical Sobolev-Hardy exponent
Chou, KS
Geng, D
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (12) : 1965 - 1984
[43] Ground State for the Schrodinger Operator with the Weighted Hardy Potential
Chabrowski, J.
Tintarev, K.
INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 2011
[44] Ground state solution for a critical Schrodinger equation involving the p-Laplacian operator and potential term
Rachid Echarghaoui
Zakaria Zaimi
Journal of Elliptic and Parabolic Equations, 2024, 10 : 475 - 497
[45] Ground state solution for a critical Schrodinger equation involving the p-Laplacian operator and potential term
Echarghaoui, Rachid
Zaimi, Zakaria
JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2024, 10 (01) : 475 - 497
[46] Multiple solutions for nonhomogeneous Choquard equation involving Hardy–Littlewood–Sobolev critical exponent
Zifei Shen
Fashun Gao
Minbo Yang
Zeitschrift für angewandte Mathematik und Physik, 2017, 68
[47] Existence and uniqueness of solutions for Choquard equation involving Hardy–Littlewood–Sobolev critical exponent
Lun Guo
Tingxi Hu
Shuangjie Peng
Wei Shuai
Calculus of Variations and Partial Differential Equations, 2019, 58
[48] Fractional Kirchhoff-type equation with Hardy-Littlewood-Sobolev critical exponent
Su, Yu
Chen, Haibo
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (06) : 2063 - 2082
[49] Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in RN
Qian, Chenyin
Shen, Zifei
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 42 : 290 - 307
[50] Nonlinear perturbations of a periodic magnetic Choquard equation with Hardy–Littlewood–Sobolev critical exponent
H. Bueno
N. da Hora Lisboa
L. L. Vieira
Zeitschrift für angewandte Mathematik und Physik, 2020, 71

← 1 2 3 4 5 →