We consider quasilinear elliptic equations involving the p-Laplacian and singular nonlinearities. We prove comparison principles and we deduce some uniqueness results.
In this paper we consider the Wos' ko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k ^ 1 for which there exists a fc-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct.
An implicit function theorem in locally convex spaces is proved. As an application we study the stability, with respect to a parameter λ, of the solutions of the Hammerstein equation x λKFx in a locally convex space.
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