Multiple existence of sign changing solutions for a nonlinear elliptic problem

Let N≥3N≥3, 20ε>0 and ΩΩ be a bounded domain with a smooth boundary ∂Ω∂Ω. Our purpose in this paper is to consider the multiple existence of sign changing solutions of the problem −ε2Δu+u=|u|p−2u,u∈H01(Ω).