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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Chen, Wenjing¹  Guerra, Ignacio² 

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

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

关键词: Multiplicity;    Bubble solutions;    Mountain pass solution;   

DOI  :  10.1016/j.jmaa.2014.11.019

来源: Elsevier

【 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.

【 授权许可】

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