For p > 2, we consider the quasilinear equation -Δpu+|u|^{p-2}u = g(u) in the unit ball B of ℝ^N, with homogeneous Neumann boundary conditions. The assumptions on g are very mild and allow the nonlinearity to be possibly supercritical in the sense of Sobolev embeddings. We prove the existence of a nonconstant, positive, radially nondecreasing solution via variational methods. In the case g(u) = |u|^{q-2}u, we detect the asymptotic behavior of these solutions as q → ∞.
A p-Laplacian supercritical Neumann problem / Colasuonno, Francesca; Noris, Benedetta. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 37:6(2017), pp. 3025-3057. [10.3934/dcds.2017130]
A p-Laplacian supercritical Neumann problem
COLASUONNO, FRANCESCA;
2017
Abstract
For p > 2, we consider the quasilinear equation -Δpu+|u|^{p-2}u = g(u) in the unit ball B of ℝ^N, with homogeneous Neumann boundary conditions. The assumptions on g are very mild and allow the nonlinearity to be possibly supercritical in the sense of Sobolev embeddings. We prove the existence of a nonconstant, positive, radially nondecreasing solution via variational methods. In the case g(u) = |u|^{q-2}u, we detect the asymptotic behavior of these solutions as q → ∞.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
