Existence of ground state solutions for a super-biquadratic Kirchhoff-type equation with steep potential well

被引：14

作者：

Du, Miao ^{[1
]}

Tian, Lixin ^{[1
]}

Wang, Jun ^{[2
]}

Zhang, Fubao ^{[3
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Jiangsu Univ, Fac Sci, Zhenjiang 212013, Peoples R China

[3] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

APPLICABLE ANALYSIS | 2016年 / 95卷 / 03期

基金：

中国博士后科学基金;

关键词：

Kirchhoff-type equation; ground state solution; Nehari manifold; variational method; 35J91; 35J20; 47J30; NONLINEAR SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; NONTRIVIAL SOLUTIONS; GLOBAL SOLVABILITY; ELLIPTIC EQUATION; BOUND-STATES; MULTIPLICITY;

D O I：

10.1080/00036811.2015.1022312

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we concern with the following Kirchhoff-type problem where a, b > 0 are constants, lambda > 0 is a parameter, V is a nonnegative continuous potential, and f is a subcritical growth nonlinearity. Under appropriate assumptions on V and f, we prove the existence of ground state solutions using variational methods. Furthermore, we also study the asymptotic behavior of ground state solutions.

引用

页码：627 / 645

页数：19

共 42 条

[1] ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTH [J].

Alves, C. O. ;

Correa, F. J. S. A. ;

Figueiredo, G. M. .

DIFFERENTIAL EQUATIONS & APPLICATIONS, 2010, 2 (03) :409-417

[2]

Alves C. O., 2001, Commun. Appl. Nonlinear Anal., V8, P43

[3] Nonlinear perturbations of a periodic Kirchhoff equation in RN [J].

Alves, Claudianor O. ;

Figueiredo, Giovany M. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (05) :2750-2759

[4] On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in RN [J].

Alves, Claudianor O. ;

Figueiredo, Giovany M. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) :1288-1311

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

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[6]

[Anonymous], 1883, Mechanik

[7]

[Anonymous], 1997, Minimax theorems

[8]

[Anonymous], 1975, MAT SB

[9] On the well-posedness of the Kirchhoff string [J].

Arosio, A ;

Panizzi, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (01) :305-330

[10] Nonlinear Schrodinger equations with steep potential well [J].

Bartsch, T ;

Pankov, A ;

Wang, ZQ .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (04) :549-569

← 1 2 3 4 5 →