Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation

Abstract

This paper is concerned with the following non linear elliptic problem involving nearly critical exponent (P^k_ε): (-Δ)^ku=K(x)|u|^{(4k/(n-1k))-ε}u in Ω, Δ^{k-1}u=…=Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in R^n, n≥ 2k+2, k≥ 1, ε is a small positive parameter and K is a smooth positive function in Ω. We construct signchanging solutions of (P^k_ε) having two bubbles and blowing up either at two different critical points of K with the same speed or at the same critical point.