The asymptotic behavior of the ground state solutions for biharmonic equations

Abstract

In this paper we study the asymptotic behavior of the ground state solutions of the Hénon type biharmonic equation Δ2u=|x|αup−1 in Ω, u>0 in Ω and u=∂u∂n=0 on ∂Ω, where Ω is the unit ball in RN, α>0,p>2. We prove that the ground state solution up concentrates on a boundary point and has a unique maximum point as p→2∗=2NN−4, which deduce that the ground state solution up is not radially symmetric.