Uniqueness of Positive Radial Solutions To Singular Critical Growth Quasilinear Elliptic Equations

Abstract: In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth [ \begin{cases} -\Delta_{p}u-{\displaystyle \frac{\mu}{|x|^{p}}|u|^{p-2}u}{\displaystyle =\frac{|u|^{\frac{(N-s)p}{N-p}-2}u}{|x|^{s}}}+\lambda|u|^{p-2}u & \text{in }B,\ u=0 & \text{on }\partial B, \end{cases} ] where $B$ is an open finite ball in $\mathbb{R}^{N}$ centered at the origin, $1<p<N$, $-\infty<\mu<((N-p)/p)^{p}$, $0\le s<p$ and $\lambda\in\mathbb{R}$. A related limiting problem is also considered.