On topological Morse theory
type: Item
instance of: scholarly article
title: On topological Morse theory
zbMATH Open document ID: 1259.58001
author: Marco Degiovanni
published in: Journal of Fixed Point Theory and Applications
publication date: 2012-11-15T00:00:00Z
review text: Some directions of research on topological critical point theory have been already performed by \textit{J.-N. Corvallec} [Z. Anal. Anwend. 16, No. 2, 405--433 (1997; Zbl 0884.58025)], \textit{A. Ioffe} and \textit{E. Schwartzman} [J. Math. Pures Appl., IX. Sér. 75, No. 2, 125--153 (1996; Zbl 0852.58018)], and \textit{G. Katriel} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11, No. 2, 189--209 (1994; Zbl 0834.58007)]. Using his previous results on Morse theory in metric spaces [``On morse theory for continuous functionals'', Conf. Semin. Math. Univ. Bari 290, 1--22 (2003)], in this interesting paper the author considers the global branch of Morse theory in the setting of metrizable topological spaces. The paper ends with a bibliography containing \(37\) suggestive references. Other author's papers directly connected to this topic are [J. Fixed Point Theory Appl. 7, No. 1, 85--102 (2010; Zbl 1205.58007); the author and \textit{S. Lancelotti}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 6, 907--919 (2007; Zbl 1132.35040); the author and \textit{M. Marzocchi}, Ann. Mat. Pura Appl., IV. Ser. 167, 73--100 (1994; Zbl 0828.58006); the author and \textit{S. Cingolani}, Commun. Partial Differ. Equations 30, No. 8, 1191--1203 (2005; Zbl 1162.35367)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 6106770
zbMATH Keywords: critical point theory
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: quasilinear elliptic equations
zbMATH Keywords: critical groups
zbMATH Keywords: Morse relations
MaRDI profile type: Publication
full work available at URL: s11784-011-0066-8
OpenAlex ID: W2033820285
cites work: Morse theory for \(C^ 1\)-functionals and Conley blocks
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: Nontrivial Solutions forp-Laplace Equations with Right-Hand Side Havingp-Linear Growth at Infinity
cites work: Morse theory for continuous functionals
cites work: A general approach to the min-max principle
cites work: On the second deformation lemma
cites work: Nontrivial solutions of quasilinear equations via nonsmooth Morse theory
cites work: On topological and metric critical point theory
cites work: Linking over cones and nontrivial solutions for \(p\)-Laplace equations with \(p\)-superlinear nonlinearity
cites work: A critical point theory for nonsmooth functionals
cites work: Bifurcation for odd potential operators and an alternative topological index
cites work: Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
cites work: On a new notion of linking and application to elliptic problems at resonance
cites work: Relative homological linking in critical point theory
cites work: On differentiable functions with isolated critical points
cites work: Q5522732
cites work: Metric critical point theory. I: Morse regularity and homotopic stability of a minimum
cites work: Mountain pass theorems and global homeomorphism theorems
cites work: Q4064160
cites work: Morse index estimates for continuous functionals associated with quasilinear elliptic equations.
cites work: A nonsymmetric asymptotically linear elliptic problem
cites work: Q4314478
cites work: Critical point theory and Hamiltonian systems
cites work: Functional Topology and Abstract Variational Theory
cites work: Functional topology and abstract variational theory
cites work: Q5564124
cites work: Morse theory on Hilbert manifolds
cites work: Homotopy theory of infinite dimensional manifolds
cites work: A generalized Morse theory
cites work: Q3749777
cites work: Q3986713
cites work: Morse theory and a non-linear generalization of the Dirichlet problem
cites work: Q5522742
DOI: 10.1007/S11784-011-0066-8
Recommended article: An application of topological equivalence to Morse theory
Recommended article: Q4389665
Recommended article: The topology of spaces of Morse functions on surfaces
Recommended article: Q4929298
Recommended article: Morse homology
Recommended article: Homolog\'ia de Morse en variedades compactas
Recommended article: MORSE HOMOLOGY ON NONCOMPACT MANIFOLDS
Recommended article: Q4939881
Recommended article: Morse homology on Hilbert spaces
Recommended article: MORSE HOMOLOGY AND MANIFOLDS WITH BOUNDARY
description: scientific article; zbMATH DE number 6106770