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

Merchán, Susana; Montoro, Luigi; Peral, Ireneo; Sciunzi, Berardino

doi:10.1016/j.anihpc.2013.01.003

Merchán, Susana ; Montoro, Luigi ; Peral, Ireneo ; Sciunzi, Berardino

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 1-22.

Résumé

In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the $- Δ_{p} (\cdot)$ operator and the Hardy–Leray potential. Assuming $0 \in Ω$ , 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.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.anihpc.2013.01.003

Classification : 35J20, 35J25, 35J62, 35J70, 35J92, 46E30, 46E35
Mots clés : 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},
     volume = {31},
     number = {1},
     year = {2014},
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     zbl = {1291.35082},
     language = {en},
     url = {http://www.numdam.org/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. http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.003/

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