Bound state solutions for Kirchhoff type equations in dimension two

被引：2

作者：

Zhang, Jian ^{[1
]}

Liu, Huize ^{[1
]}

Bao, Xue ^{[1
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 507卷 / 02期

关键词：

Kirchhoff type equation; Bound states; Dimension two; Variational method; NONLINEAR SCHRODINGER-EQUATION; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; GROUND-STATES; EXISTENCE;

D O I：

10.1016/j.jmaa.2021.125796

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 Kirchhoff type equation: -M (integral(R2) vertical bar del u vertical bar(2)dx) Delta u + u = a(x) f(u) in R-2, where M is a general function with inf(R+) M > 0 and f is a superlinear subcritical term. We obtain bound state solutions by developing some techniques in variational methods. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：18

共 27 条

[1] Bending and stretching energies in a rectangular plate modeling suspension bridges [J].

Al-Gwaiz, Mohammed ;

Benci, Vieri ;

Gazzola, Filippo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 106 :18-34

[2] A note on the elliptic Kirchhoff equation in RN perturbed by a local nonlinearity [J].

Azzoilini, A. .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2015, 17 (04)

[3] On the existence of a positive solution of semilinear elliptic equations in unbounded domains [J].

Bahri, A ;

Lions, PL .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (03) :365-413

[4] EXISTENCE OF POSITIVE SOLUTIONS OF THE EQUATION -DELTA-U+A(X)U=U(N+2)/(N-2) IN RN [J].

BENCI, V ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) :90-117

[5] The effect of concentrating potentials in some singularly perturbed problems [J].

Cerami, G ;

Passaseo, D .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 17 (03) :257-281

[6] Positive bound state solutions for some Schrodinger-Poisson systems [J].

Cerami, Giovanna ;

Molle, Riccardo .

NONLINEARITY, 2016, 29 (10) :3103-3119

[7] Positive solutions for some non-autonomous Schrodinger-Poisson systems [J].

Cerami, Giovanna ;

Vaira, Giusi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (03) :521-543

[8] Ground state solutions for Kirchhoff-type equations with general nonlinearity in low dimension [J].

Chen, Jing ;

Li, Yiqing .

BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)

[9] On the planar Schrodinger-Poisson system [J].

Cingolani, Silvia ;

Weth, Tobias .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (01) :169-197

[10] ELLIPTIC-EQUATIONS IN R(2) WITH NONLINEARITIES IN THE CRITICAL GROWTH RANGE [J].

DEFIGUEIREDO, DG ;

MIYAGAKI, OH ;

RUF, B .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1995, 3 (02) :139-153

← 1 2 3 →