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

Abstract

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 continuous function.