Ukrainian Mathematical Journal

, Volume 60, Issue 1, pp 114–120 | Cite as

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

  • A. K. Prykarpats’kyi


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.


Banach Space Nonlinear Functional Analysis Ulam Theorem Solution Manifold Linear Continuous Projector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • A. K. Prykarpats’kyi
    • 1
  1. 1.Institute of Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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