Geodesic
Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 1-22

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In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the -Δ p (·) 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.

DOI : 10.1016/j.anihpc.2013.01.003
Classification : 35J20, 35J25, 35J62, 35J70, 35J92, 46E30, 46E35
Keywords: Quasilinear elliptic equations, Hardy potential, Supercritical problems, Existence and nonexistence, Regularity, Symmetry of solutions 
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     author = {Merch\'an, Susana and Montoro, Luigi and Peral, Ireneo and Sciunzi, Berardino},
     title = {Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the {Hardy{\textendash}Leray} potential},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1--22},
     publisher = {Elsevier},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.01.003/}
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Merchán, Susana; Montoro, Luigi; Peral, Ireneo; Sciunzi, Berardino. Existence and qualitative properties of solutions to a quasilinear elliptic equation involving the Hardy–Leray potential. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 1-22. doi: 10.1016/j.anihpc.2013.01.003

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