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

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