## Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy-Leray potential.(English)Zbl 1291.35082

Summary: In this work, we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the $$-\Delta p(\cdot )$$ operator and the Hardy-Leray potential. Assuming $$0\in\varOmega$$, 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.

### MSC:

 35J62 Quasilinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35J70 Degenerate elliptic equations 35J92 Quasilinear elliptic equations with $$p$$-Laplacian 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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### References:

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