LAUSR

Abstract We establish the existence of a non-trivial weak solution to the following singular quasilinear equation with Hardy potential and singular quadratic gradient term: { − Δ u − μ u | x | 2 = | ∇ u | 2 u + f ( x , u ) in Ω , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R N is a smooth bounded domain, μ > 0 , 0 ∈ Ω , N ≥ 3 . We show that there exists a solution u ∈ H 0 1 ( Ω ) to the above problem. The notable characteristic of this problem is that it includes quadratic gradient nonlinearity and strong singularity.