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Leggett-Williams norm-type theorems for coincidences

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We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14].

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Correspondence to Donal O’Regan.

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Received: 9 July 2005; revised: 12 January 2006

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O’Regan, D., Zima, M. Leggett-Williams norm-type theorems for coincidences. Arch. Math. 87, 233–244 (2006).

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Mathematics Subject Classification (2000).