Some existence results for duality mappings

Existence results for the equation Ju = Nu are given; here J : X --> X* is a duality mapping on a reflexive Banach space and N : Z --> Z* is a demicon tinuous operator Z being a Banach space such that X is compactly imbedded i n Z. As examples, the existence of a W-0(1,P)-solution, 1 < p < infinity, i s proved in an unitary manner for J being the p-Laplacian, the A(p)-Laplaci an or the pseudo-laplacian and for N = N-f being a Nemitsky operator corres ponding to a Caratheodory function f : Omega x R --> R which satisfies a pa rticular growth condition. (C) Academie des Sciences/Elsevier, Paris.