A Resonant-Superlinear Elliptic Problem Revisited
Résumé
We consider the resonant-superlinear elliptic problem−∆u=λ1u+(u+)q+f(x), withDirichlet boundary conditions on a bounded regular domain ofRN. We assume that 1Nsatisfies∫Ωfφ1<0 and (λ1,φ1) is the first eigenpair of−∆onH10(Ω). We apply a non-well ordered lower and upper solution result on a family ofmodified problems and obtain a sequence of localized solutions of these modified problems.Thanks to this localization and a precise bootstrap argument we are abble to prove that forlarge modification, these solutions are, in fact, solutions of our initial problem.The problem was already considered in [2] by a totally different approach.