The asymptotic behavior of the ground state solutions for biharmonic equations Original Research Article

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