Singular elliptic equations with quadratic gradient term

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:{−Δu−μu|x|2=|∇u|2u+f(x,u)inΩ,u>0inΩ,u=0on∂Ω, where Ω⊂RN is a smooth bounded domain, μ>0,0∈Ω,N≥3. We show that there exists a solution u∈H01(Ω) to the above problem. The notable characteristic of this problem is that it includes quadratic gradient nonlinearity and strong singularity.