Leggett-Williams norm-type theorems for coincidences |
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| Authors: | Donal O’Regan Mirosława Zima |
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| Institution: | (1) Department of Mathematics, National University of Ireland, Galway, Ireland;(2) Institute of Mathematics, University of Rzeszów, Rejtana 16 A, PL-35-310 Rzeszów, Poland |
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| Abstract: | 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].
Received: 9 July 2005; revised: 12 January 2006 |
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| Keywords: | 47H07 47H09 34B18 34C25 |
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