2017
Том 69
№ 9

All Issues

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

Prikarpatskii A. K.

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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.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 1, pp 114-120.

Citation Example: Prikarpatskii A. K. An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications // Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 100–106.

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