par Gossez, Jean-Pierre ;Arias, Maite;Campos, Juan Manuel;Cuesta, M.
Référence Annales de l'Institut Henri Poincaré. Analyse non linéaire, 19, page (581-616)
Publication Publié, 2002
Article révisé par les pairs
Résumé : We prove the existence of a first nontrivial eigenvalue for an asymmetric elliptic problem with weights involving the laplacian (cf. (1.2) below) or more generally the p-laplacian (cf. (1.3) below). A first application is given to the description of the beginning of the Fučik spectrum with weights for these operators. Another application concerns the study of nonresonance for the problems (1.1) and (1.5) below. One feature of our nonresonance conditions is that they involve eigenvalues with weights instead of pointwise restrictions. © 2002 Éditions scientifiques et médicales Elsevier SAS.