Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential

In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the −Δp(⋅) operator and the Hardy–Leray potential. Assuming 0∈Ω, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry.