Topological characteristics of extremals of variational problems
type: Item
instance of: scholarly article
title: Topological characteristics of extremals of variational problems
zbMATH Open document ID: 0853.58040
DOI: 10.1007/BF02362948
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-01-05T00:00:00Z
review text: In this extensive review, the author describes methods of investigating variational problems based on the concepts of topological index, Euler characteristic and Lyusternik-Schnirelman category. These methods are used to prove a variety of necessary and sufficient conditions of optimality, to estimate the number of critical points and critical solutions and to validate approximate algorithms for the construction of solutions of variational problems. The authors show that the methods not only extend the boundaries of the applicability of the classical methods but also make essential contributions to the task of solving those classical problems for which the classical theory is inadequate. The work contains an extensive bibliography with 219 entries.
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 889755
zbMATH Keywords: topological index
zbMATH Keywords: Euler characteristic
zbMATH Keywords: Lyusternik-Schnirelman category
zbMATH Keywords: critical points
zbMATH Keywords: bibliography
author: N. A. Bobylev
author: S. K. Korovin
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
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Topological characteristics of extremals of variational problems (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02362948

Topological characteristics of extremals of variational problems (OpenAlex ID)
OpenAlex ID: W4237863515

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