Bubbles tower solutions to a fourth-order elliptic equation with subcritical nonlinearity

Abstract

This paper is concerned with the nonlinear elliptic problem involving nearly critical exponent (Pε): Δ2u=K|u|(8/(n−4))−εu in Ω, Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in Rn, n≥ 5, ε is a small positive parameter and K is a C3 positive function on Ω¯. As ε goes to zero, we construct a solution with the shape of a tower of sign changing bubbles.