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Leggett-Williams norm-type theorems for coincidences

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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].

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  2. Institute of Mathematics, University of Rzeszów, Rejtana 16 A, PL-35-310, Rzeszów, Poland

    Mirosława Zima

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  1. Donal O’Regan
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  2. Mirosława Zima
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Correspondence to Donal O’Regan.

Additional information

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). https://doi.org/10.1007/s00013-006-1661-6

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  • DOI: https://doi.org/10.1007/s00013-006-1661-6

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