Geodesic
Multiplicity of Solutions on a Nehari Set in an Invariant Cone
Minimax theory and its applications, Tome 7 (2022) no. 2
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For 1 < p <2 and q large, we prove the existence of two positive, nonconstant, radial and radially nondecreasing solutions of the supercritical equation −∆pu+up−1 =uq−1 under Neumann boundary conditions, in the unit ball of RN. We use a variational approach in an invariant cone. We distinguish the two solutions upon their energy: one is a ground state inside a Nehari-type subset of the cone, the other is obtained via a mountain pass argument inside the Nehari set.
Mots-clés : Quasilinear elliptic equations, Sobolev-supercritical nonlinearities, Neumann boundary conditions, Radial solutions 
@article{MTA_2022_7_2_a1,
     author = {Francesca Colasuonno,Benedetta Noris and Gianmaria Verzini},
     title = {Multiplicity of {Solutions} on a {Nehari} {Set} in an {Invariant} {Cone}},
     journal = {Minimax theory and its applications},
     year = {2022},
     volume = {7},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a1/}
}
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Francesca Colasuonno,Benedetta Noris; Gianmaria Verzini. Multiplicity of Solutions on a Nehari Set in an Invariant Cone. Minimax theory and its applications, Tome 7 (2022) no. 2. http://geodesic.mathdoc.fr/item/MTA_2022_7_2_a1/