The Asymptotic Behavior Of The Ground State Solutions For A Glass Of Equations Of P-Laplace Type

The main purpose of this paper is to analyze the asymptotic behavior of the ground state solution of the following elliptic equation of p-Laplacian typewhereΩis a ball in Rⁿ centered at the origin ,α> 0 , 1 < p < q < p* = np/n-p andâ–³_pu = div(|â–½u|^p-2â–½u) is the p-Laplacian of u . We prove that if u^q is a ground state solution of (*) , then u_q has some maximum point x_q∈Ωwith dist(x_q, (?)Ω)→0 as q→p^* . The asymptotic behavior of ground state solution u_q is also given .This paper is organized as follows : In section 1 , we introduce the research background about Henon equation and main results . In section 2 , we give some preliminaries of this paper . In section 3 , we prove Proposition 1.3 by the concentration compactness principle argument . In section 4 , we prove Theorem 1.4 mainly by Blow -up method .