Some existence results for duality mappings
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文摘
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 demicontinuous operator, Z being a Banach space such that X is compactly imbedded in Z. As examples, the existence of a W1,p0-solution, 1 < p < ∞, is proved in an unitary manner for J being the p-Laplacian, the Ap-Laplacian or the pseudo-Laplacian and for N = Nf being a Nemitsky operator corresponding to a Carathéodory function f : Ω × R → R which satisfies a particular growth condition.