Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential

被引：5

作者：

Zhang, Danqing ^{[1
]}

Chai, Guoqing ^{[1
]}

Liu, Weiming ^{[1
]}

机构：

[1] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2017年

基金：

中国国家自然科学基金;

关键词：

Kirchhoff equation; variational methods; concentration; GROUND-STATE SOLUTIONS; HIGH-ENERGY SOLUTIONS; POSITIVE SOLUTIONS; R-N; NODAL SOLUTIONS; MULTIPLICITY; R-3; BEHAVIOR; GROWTH;

D O I：

10.1186/s13661-017-0875-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following nonlinear problem of Kirchhoff type: {-(a + b integral(R3) |del u|(2)) Delta u + lambda V(x)u = |u|(p-2)u, in R-3, u is an element of H-1(R-3), where the parameter lambda > 0 and 4 <= p < 6, constants a, b > 0. By variational methods, the results of the existence of nontrivial solutions and the concentration phenomena of the solutions as lambda -> +infinity are obtained. It is worth pointing out that, for the case p is an element of (4, 6), the potential V is permitted to be sign-changing.

引用

页数：15

共 28 条

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