Singular elliptic equations with quadratic gradient term

We establish the existence of a non-trivial weak solution to the following singular quasilinear equation with Hardy potential and singular quadratic gradient term: [Formula presented] where Ω⊂R^N is a smooth bounded domain, μ>0,0∈Ω,N≥3. We show that there exists a solution u∈H<inf>0</inf>¹(Ω) to the above problem. The notable characteristic of this problem is that it includes quadratic gradient nonlinearity and strong singularity.