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, Volume 31 (2014) no. 1, p. 1-22

In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the $-{\Delta }_{p}\left(·\right)$ operator and the Hardy–Leray potential. Assuming $0\in \Omega$, 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 : https://doi.org/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
@article{AIHPC_2014__31_1_1_0,
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--Leray potential},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {31},
number = {1},
year = {2014},
pages = {1-22},
doi = {10.1016/j.anihpc.2013.01.003},
zbl = {1291.35082},
mrnumber = {3165277},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2014__31_1_1_0}
}

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, Volume 31 (2014) no. 1, pp. 1-22. doi : 10.1016/j.anihpc.2013.01.003. http://www.numdam.org/item/AIHPC_2014__31_1_1_0/

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