Abstract
We prove the existence of a first nonprincipal eigenvalue for an asymmetric Neumann problem with weights involving the p-Laplacian (cf. (1.2) below). As an application we obtain a first nontrivial curve in the corresponding Fučik spectrum (cf. (1.4) below). The case where one of the weights has meanvalue zero requires some special attention in connexion with the (PS) condition and with the mountain pass geometry.
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