On the radial solutions of a p-Laplace equation with the Hardy potential

Abstract

In this paper, we study the asymptotic behavior of radial solutions of the following quasi-linear equation with the Hardy potential Δpu+h(|x|)|u|p−2u=0, x∈RN−{0}, where 2<p<N, h is a radial function on RN−{0} such that h(|x|)=γ|x|−p, γ>0 and Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator. The study strongly depends on the sign of γ−(σ/p∗)p where σ=(N−p)/(p−1) and p∗=p/(p−1).