Existence and asymptotics of solutions to a p-Laplacian Neumann problem through a Nehari-type set in an invariant cone
Venue: Benedetta Noris - Luogo: Aula Lagrange (Dipartimento di Matematica, Università di Torino)
We consider a p-Laplacian equation for 1<p<2, with nonlinearity of pure power type with exponent q. We search for nonconstant, radial and radially nondeacreasing solutions in a ball, with Neumann boundary conditions. For large values of q, we prove the existence of two distinct solutions of this type, by making use of 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. As a byproduct of our proof, we show that the constant solution 1 is a local minimum on the Nehari set. In addition, we detect the limit profiles of the two nonconstant solutions as q tends to infinity.
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