Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth

被引：5

作者：

Lei, Jun ^{[1
]}

Suo, Hongmin ^{[1
]}

机构：

[1] Guizhou Minzu Univ, Sch Data Sci & Informat Engn, Guiyang 550025, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff type equation; Neumann problem; critical growth; variation methods; nontrivial solution; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; EXISTENCE;

D O I：

10.3934/math.2021227

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a Neumann problem of Kirchhoff type equation {-(a+b integral(Omega) vertical bar del vertical bar(2) dx)Delta u + u = Q(x)vertical bar u vertical bar(4)u + lambda P(x)vertical bar u vertical bar(q-2)u, in Omega, partial derivative u/partial derivative v = 0, on partial derivative Omega, where Omega subset of R-3 is a bounded domain with a smooth boundary, a, b > 0, 1 < q < 2, lambda > 0 is a real parameter, Q(x) and P(x) satisfy some suitable assumptions. By using the variational method and the concentration compactness principle, we obtain the existence and multiplicity of nontrivial solutions.

引用

页码：3821 / 3837

页数：17

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