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 37 条

[1]

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

[2]

Alves C. O., 2015, PREPRINT

[3]

Alves CO, 2006, ADV NONLINEAR STUD, V6, P491

[4] 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

[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, VORLESUNGEN MATH PHY

[7]

Azzollini A, 2012, DIFFER INTEGRAL EQU, V25, P543

[8]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[9] On a Schrodinger-Kirchhoff-type equation involving the p(x)-Laplacian [J].

Cammaroto, F. ;

Vilasi, L. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 81 :42-53

[10] Multiple solutions for p-Kirchhoff equations in RN [J].

Chen, Caisheng ;

Song, Hongxue ;

Xiu, Zhonghu .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 86 :146-156

← 1 2 3 4 →