Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential

Chang-Lin Xiang

Published 2015-02-13Version 1

Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \[-\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\,x\in \mathbb{R}^{N},\] where $1<p<N, 0\leq\mu<\left({(N-p)}/{p}\right)^{p}$ and $Q\in L^{\infty}(\mathbb{R}^{N})$.