THE RELATION BETWEEN THE NONLINEAR ANALYSIS, BIFURCATIONS AND NONLINEAR DYNAMICS (On the example of Voronezh school of nonlinear functional analysis)
Cite this article as:
Mukhin R. R. THE RELATION BETWEEN THE NONLINEAR ANALYSIS, BIFURCATIONS AND NONLINEAR DYNAMICS (On the example of Voronezh school of nonlinear functional analysis). Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 6, pp. 74-88. DOI: https://doi.org/10.18500/0869-6632-2015-23-6-74-88
The paper is devoted to some historical aspects of the rapidly developing field of modern mathematics – nonlinear functional analysis, which is presented as the basis of the mathematical apparatus of nonlinear dynamics. Its methods are demonstrated on the example of bifurcation. The first bifurcations problem – Euler problem on elastic instability rod under longitudinal compressive forces is considered. The formation of Voronezh school of functional analysis and its role in the development of nonlinear analysis in general is also discussed.
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BibTeX
author = {R. R. Mukhin},
title = {THE RELATION BETWEEN THE NONLINEAR ANALYSIS, BIFURCATIONS AND NONLINEAR DYNAMICS (On the example of Voronezh school of nonlinear functional analysis)},
year = {2015},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {23},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/the-relation-between-the-nonlinear-analysis-bifurcations-and-nonlinear-dynamics-on-the},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2015-23-6-74-88},pages = {74--88},issn = {0869-6632},
keywords = {Nonlinear functional analysis,Banach space,nonlinear operator,bifurcation,instability,Voronezh school of functional analysis,Soviet mathematics,Krasnosel’skii theorem.},
abstract = {The paper is devoted to some historical aspects of the rapidly developing field of modern mathematics – nonlinear functional analysis, which is presented as the basis of the mathematical apparatus of nonlinear dynamics. Its methods are demonstrated on the example of bifurcation. The first bifurcations problem – Euler problem on elastic instability rod under longitudinal compressive forces is considered. The formation of Voronezh school of functional analysis and its role in the development of nonlinear analysis in general is also discussed. Download full version }}