Multiplicity of Solutions on a Nehari Set in an Invariant Cone
Keywords:
Quasilinear elliptic equations, Sobolev-supercritical nonlinearities, Neumann boundary conditions, Radial solutions.Abstract
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.
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