Multiple existence of sign changing solutions for a nonlinear elliptic problem

Abstract

Let N ≥ 3 , 2 < p < 2 ∗ = 2 N / ( N − 2 ) , ε > 0 and Ω be a bounded domain with a smooth boundary ∂ Ω . Our purpose in this paper is to consider the multiple existence of sign changing solutions of the problem − ε 2 Δ u + u = | u | p − 2 u , u ∈ H 0 1 ( Ω ) .