AN INFINITE-DIMENSIONAL BORSUK-ULAM-TYPE GENERALIZATION OF THE LERAY-SCHAUDER FIXED-POINT THEOREM AND SOME APPLICATIONS

被引：7

作者：

Prykarpats'kyi, A. K. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Problems Mech & Math, Lvov, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2008年 / 60卷 / 01期

关键词：

Banach Space; Nonlinear Functional Analysis; Ulam Theorem; Solution Manifold; Linear Continuous Projector;

D O I：

10.1007/s11253-008-0046-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：114 / 120

页数：7

共 37 条

[1] An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications
A. K. Prykarpats’kyi
[J]. Ukrainian Mathematical Journal, 2008, 60 : 114 - 120
[2] On fixed point theorems of Leray-Schauder type
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[6] Generalizations of the Nonlinear Henry Inequality and the Leray-Schauder Type Fixed Point Theorem with Applications to Fractional Differential Inclusions
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[J]. FRACTAL AND FRACTIONAL, 2021, 5 (04)
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[8] On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
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[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2019, 53 (01) : 61 - 64
[9] A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps
Gel'man, B. D.
[J]. SBORNIK MATHEMATICS, 2016, 207 (06) : 841 - 853
[10] On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
B. D. Gel’man
[J]. Functional Analysis and Its Applications, 2019, 53 : 61 - 64

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