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

TL;DR

This paper derives optimal asymptotic estimates for weak solutions of a class of quasilinear elliptic equations with Hardy potential, analyzing their behavior near the origin and at infinity.

Contribution

It provides new precise asymptotic estimates for solutions to quasilinear elliptic equations involving Hardy potentials, extending understanding of their behavior.

Findings

Established optimal decay rates at infinity.

Determined singularity behavior near the origin.

Extended previous results to broader parameter ranges.

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 nonlinear function.