JournalsaihpcVol. 31, No. 1pp. 1–22

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

  • Luigi Montoro

    Dipartimento di Matematica, UNICAL, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende, Cosenza, Italy

  • Ireneo Peral

    Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

  • Berardino Sciunzi

    Dipartimento di Matematica, UNICAL, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende, Cosenza, Italy

  • Susana Merchán

    Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential cover
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Abstract

In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the operator and the Hardy–Leray potential. Assuming , 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.

Cite this article

Luigi Montoro, Ireneo Peral, Berardino Sciunzi, Susana Merchán, Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 1, pp. 1–22

DOI 10.1016/J.ANIHPC.2013.01.003