On a class of quasilinear elliptic equations with double singularity and quadratic convection term

In this paper, we study existence and summability of distributional solutions in H₀¹(Ω ) H 0 1 ( Ω ) or H¹loc(Ω ) H loc 1 ( Ω ) to a class of quasilinear stationary Schrödinger equations with double singularities and a quadratic convection term. The results obtained depend on the summability of a datum g ( x ) (which belongs to a Lebesgue space) and on a parameter λ λ of a singular term. In particular, we establish the existence of distributional solutions in H₀¹(Ω ) H 0 1 ( Ω ) for weak and strongly singular nonlinearities.