Multi-bump solutions for a Kirchhoff-type problem

被引：37

作者：

Alves, Claudianor O. ^{[1
]}

Figueiredo, Giovany M. ^{[2
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429900 Campina Grande, PB, Brazil

[2] Fed Univ Para, Fac Matemat, BR-66075110 Belem, Para, Brazil

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2016年 / 5卷 / 01期

关键词：

Kirchhoff problem; multi-bump solution; variational methods; SIGN-CHANGING SOLUTIONS; POSITIVE SOLUTIONS; CONCENTRATION BEHAVIOR; ELLIPTIC EQUATION; EXISTENCE; MULTIPLICITY;

D O I：

10.1515/anona-2015-0101

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of solutions for the Kirchhoff problem {M(integral(R3)vertical bar del u vertical bar(2) dx + integral(R3) (lambda a(x) + 1)u(2) dx)(-Delta u + (lambda a(x) + 1)u) = f(u) in R-3, u is an element of H-1(R-3). Assuming that the nonnegative function a(x) has a potential well with int(a(-1) ({0})) consisting of k disjoint components Omega(1), Omega(2), ... , Omega(k) and the nonlinearity f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by using variational methods.

引用

页码：1 / 26

页数：26

共 50 条

[31] Multiplicity and concentration behavior of solutions to the critical Kirchhoff-type problem [J].

Zhang, Jian ;

Zou, Wenming .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2017, 68 (03)

[32] Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains [J].

Shuai, Wei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (04) :1256-1274

[33] Existence of solutions for a class of Kirchhoff-type equations with indefinite potential [J].

Zhou, Jian ;

Wu, Yunshun .

BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)

[34] Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p-Laplacian [J].

Kang, Danyang ;

Liu, Cuiling ;

Zhang, Xingyong .

MATHEMATICS, 2020, 8 (01)

[35] On the eigenvalue problem for a class of Kirchhoff-type equations [J].

Mende, Osvaldo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 494 (02)

[36] Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition [J].

Chaharlang, Moloud Makvand ;

Razani, Abdolrahman .

GEORGIAN MATHEMATICAL JOURNAL, 2021, 28 (03) :429-438

[37] Multiple solutions for Kirchhoff-type equations in RN [J].

Ye, Yiwei ;

Tang, Chun-Lei .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (08)

[38] On ground states for the Kirchhoff-type problem with a general critical nonlinearity [J].

Liu, Zhisu ;

Guo, Shangjiang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 426 (01) :267-287

[39] NEW TYPE OF MULTI-BUMP SOLUTIONS FOR SCHRODINGER-POISSON SYSTEMS [J].

Wang, Tao ;

Tian, Xiaoyu ;

He, Wenling .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 2025 (72) :1-14

[40] A fractional Kirchhoff-type problem in RN without the (AR) condition [J].

Xiang, Mingqi ;

Zhang, Binlin ;

Yang, Miaomiao .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (11) :1481-1493

← 1 2 3 4 5 →