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An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications

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Abstract

A generalization of the classical Leray-Schauder fixed-point theorem based on the infinite-dimensional Borsuk-Ulam-type antipode construction is proposed. A new nonstandard proof of the classical Leray-Schauder fixed-point theorem and a study of the solution manifold of a nonlinear Hamilton-Jacobi-type equation are presented.

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    A. K. Prykarpats’kyi

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  1. A. K. Prykarpats’kyi
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 100–106, January, 2008.

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Prykarpats’kyi, A.K. An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications. Ukr Math J 60, 114–120 (2008). https://doi.org/10.1007/s11253-008-0046-3

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  • DOI: https://doi.org/10.1007/s11253-008-0046-3

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