A Note on Asymptotic Behaviors Of Solutions To Quasilinear Elliptic Equations with Hardy Potential

Cheng-Jun He, Chang-Lin Xiang

Published 2015-01-08Version 1

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \begin{eqnarray*} -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), & & x\in\R^{N}, \end{eqnarray*} where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$, $m>0$ and $f$ is a nonlinear function.