par Gossez, Jean-Pierre ;De Figueiredo, D.;Ubilla, P.
Référence Journal of functional analysis, 257, page (721-752)
Publication Publié, 2009
Article révisé par les pairs
Résumé : We study the existence, nonexistence and multiplicity of positive solutions for a family of problems - Δp u = fλ (x, u), u ∈ W01, p (Ω), where Ω is a bounded domain in RN, N > p, and λ > 0 is a parameter. The family we consider includes the well-known nonlinearities of Ambrosetti-Brezis-Cerami type in a more general form, namely λ a (x) uq + b (x) ur, where 0 ≤ q < p - 1 < r ≤ p* - 1. Here the coefficient a (x) is assumed to be nonnegative but b (x) is allowed to change sign, even in the critical case. Preliminary results of independent interest include the extension to the p-Laplacian context of the Brezis-Nirenberg result on local minimization in W01, p and C01, a C1, α estimate for equations of the form - Δp u = h (x, u) with h of critical growth, a strong comparison result for the p-Laplacian, and a variational approach to the method of upper-lower solutions for the p-Laplacian. © 2009 Elsevier Inc. All rights reserved.