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An extension of the topological degree in Hilbert space

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  • J. Berkovits
  • C. Fabry

Abstract

We define classes of mappings of monotone type with respect to a given direct sum decomposition of the underlying Hilbert space H . The new classes are extensions of classes of mappings of monotone type familiar in the study of partial differential equations, for example, the class ( S + ) and the class of pseudomonotone mappings. We then construct an extension of the Leray-Schauder degree for mappings involving the above classes. As shown by (semi-abstract) examples, this extension of the degree should be useful in the study of semilinear equations, when the linear part has an infinite-dimensional kernel.

Suggested Citation

  • J. Berkovits & C. Fabry, 2005. "An extension of the topological degree in Hilbert space," Abstract and Applied Analysis, Hindawi, vol. 2005, pages 1-17, January.
    • Handle: RePEc:hin:jnlaaa:438469
    DOI: 10.1155/AAA.2005.581
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