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Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents $$ \textstyle\begin{cases} -\Delta_{p}u-\mu \frac{ \vert u \vert ^{p-2}u}{ \vert x \vert ^{p}}=Q(x) \frac{ \vert u \vert ^{p^{*}(t)-2}u}{ \vert x \vert ^{t}}+\lambda u^{-s}, &\text{in }\Omega , \\ u>0, & \text{in }\Omega , \\ u=0, &\text{on }\partial \Omega …