Multiplicity of Solutions to Nearly Critical Elliptic Equation in the Bounded Domain of r3

We consider the following Dirichlet boundary value problem. (0.1){-δu=u5-ε+λuq,u>0in Ωu=0on ∂Ω, where Ω is a smooth bounded domain in R3, 1. <. q<. 3, the parameters λ. >. 0 and ε. >. 0. By Lyapunov-Schmidt reduction method and the Mountain Pass Theorem, we prove that in suitable ranges for the parameters λ and ε, 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 subcritical problem with an increasing nonlinearity. © 2014 Elsevier Inc.