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A P-laplacian Neumann problem with a possibly supercritical nonlinearity

par Colasuonno, Francesca
Référence Rendiconti del seminario matematico, 74, 3-4, page (113-122)
Publication Publié, 2016

Article révisé par les pairs

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Résumé :

We look for nonconstant, positive, radial, radially nondecreasing solutions of the quasilinear equation-Δpu + up-1 = f(u) with p > 2, in the unit ball B of ℝN, subject to homogeneous Neumann boundary conditions. The assumptions on the nonlinearity f are very mild and allow it to be possibly supercritical in the sense of Sobolev embeddings. The main tools used are the truncation method and a mountain pass-type argument. In the pure power case, i.e., f(u) = uq-1, we detect the limit profile of the solutions of the problems as q → ∞. These results are proved in [3], in collaboration with B. Noris.