New results on the existence of ground state solutions for generalized quasilinear Schrodinger equations coupled with the Chern-Simons gauge theory

被引：3

作者：

Xiao, Yingying ^{[1
,2
]}

Zhu, Chuanxi ^{[1
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

[2] Nanchang JiaoTong Inst, Nanchang 330031, Jiangxi, Peoples R China

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2021年 / 73期

基金：

中国国家自然科学基金;

关键词：

gauged Schrodinger equation; Pohozaev identity; ground state solutions; STANDING WAVES; SYSTEM;

D O I：

10.14232/ejqtde.2021.1.73

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following quasilinear Schrodinger equation -Delta u + V(x)u-ku Delta(u(2)) + mu h(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) (1 + ku(2))u + mu(integral(+infinity)(vertical bar x vertical bar) h(s)/s (2 + ku(2)(s))u(2)(s)ds) u = f (u) in R-2, where k > 0, mu > 0, V is an element of C-1 (R-2, R) and f is an element of C(R, R). By using a constraint minimization of Pohozaev-Nehari type and analytic techniques, we obtain the existence of ground state solutions.

引用

页码：1 / 17

页数：17

共 35 条

[1] On standing waves with a vortex point of order N for the nonlinear Chern-Simons-Schrodinger equations [J].

Byeon, Jaeyoung ;

Huh, Hyungjin ;

Seok, Jinmyoung .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (02) :1285-1316

[2] Standing waves of nonlinear Schrodinger equations with the gauge field [J].

Byeon, Jaeyoung ;

Huh, Hyungjin ;

Seok, Jinmyoung .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (06) :1575-1608

[3] Existence and concentration of semiclassical ground state solutions for the generalized Chern-Simons-Schrodinger system in H1 (R2) [J].

Chen, Sitong ;

Zhang, Binlin ;

Tang, Xianhua .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 185 :68-96

[4] Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity [J].

Chen, Sitong ;

Zhang, Binlin ;

Tang, Xianhua .

ADVANCES IN NONLINEAR ANALYSIS, 2020, 9 (01) :148-167

[5] AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRODINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES [J].

Chen, Sitong ;

Gao, Zu .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (02) :231-241

[6] Sign-changing multi-bump solutions for the Chern-Simons-Schrodinger equations in R2 [J].

Chen, Zhi ;

Tang, Xianhua ;

Zhang, Jian .

ADVANCES IN NONLINEAR ANALYSIS, 2020, 9 (01) :1066-1091

[7] A multiplicity result for Chern-Simons-Schrodinger equation with a general nonlinearity [J].

Cunha, Patricia L. ;

d'Avenia, Pietro ;

Pomponio, Alessio ;

Siciliano, Gaetano .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (06) :1831-1850

[8] Standing waves of modified Schrodinger equations coupled with the Chern-Simons gauge theory [J].

d'Avenia, Pietro ;

Pomponio, Alessio ;

Watanabe, Tatsuya .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2020, 150 (04) :1915-1936

[9] Nodal standing waves for a gauged nonlinear Schrodinger equation in R2 [J].

Deng, Yinbin ;

Peng, Shuangjie ;

Shuai, Wei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (06) :4006-4035

[10] Energy Solution to the Chern-Simons-Schrodinger Equations [J].

Huh, Hyungjin .

ABSTRACT AND APPLIED ANALYSIS, 2013,

← 1 2 3 4 →