Multiplicity of solutions to nearly critical elliptic equation in the bounded domain of R3

被引：1

作者：

Chen, Wenjing ^{[1
]}

Guerra, Ignacio ^{[2
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Santiago 9170125, Chile

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 424卷 / 01期

关键词：

Multiplicity; Bubble solutions; Mountain pass solution; CRITICAL SOBOLEV EXPONENT; NEUMANN PROBLEM; GROUND-STATES; GROWTH;

D O I：

10.1016/j.jmaa.2014.11.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following Dirichlet boundary value problem {-Delta u = u(5-epsilon) + lambda u(q), u > 0 in Omega; u = 0 on partial derivative Omega, (0.1) where Omega is a smooth bounded domain in R-3, 1 < q < 3, the parameters lambda > 0 and epsilon > 0. By Lyapunov-Schmidt reduction method and the Mountain Pass Theorem, we prove that in suitable ranges for the parameters lambda and epsilon, problem (0.1) has at least two solutions. Additionally if 2 <= q < 3, we prove the existence of at least three solutions. Consequently, we prove a non-uniqueness result for a suberitical problem with an increasing nonlinearity. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：179 / 200

页数：22

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