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;
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 → ∞.File in questo prodotto:
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