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Stratified Morse Theory in Arrangements [PDF]
Pure and Applied Mathematics Quarterly, 2006 This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement.
Cohen, Daniel C., Orlik, Peter
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Fundamental theorems of Morse theory on posets
AIMS Mathematics, 2022 We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities in ...
D. Fernández-Ternero +3 more
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On the Morse–Novikov Cohomology of blowing up complex manifolds
Comptes Rendus. Mathématique, 2020 Inspired by the recent works of S. Rao–S. Yang–X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse–Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse–Novikov cohomology by introducing the relative ...
Zou, Yongpan
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Morse potential specific heat with applications: an integral equations theory based
BMC Chemistry, 2022 The specific heat in its molar form or mass form is a significant thermal property in the study of the thermal capacity of the described system. There are two basic methods for the determination of the molar specific heat capacity, one of them is the ...
Marwan Al-Raeei
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Multiple solutions for a coercive quasilinear elliptic equation via Morse theory
Boundary Value Problems, 2021 We study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.
Lifang Fu, Mingzheng Sun
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Functoriality and duality in Morse-Conley-Floer homology [PDF]
, 2014 In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory.
Rot, T. O., Vandervorst, R. C. A. M.
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Results on multiple nontrivial solutions to partial difference equations
AIMS Mathematics, 2023 In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory.
Huan Zhang , Yin Zhou, Yuhua Long
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Multiple periodic solutions of nonlinear second order differential equations
AIMS Mathematics, 2023 In this paper, we are interested in the existence of multiple nontrivial $ T $-periodic solutions of the nonlinear second ordinary differential equation $ \ddot{x}+V_x(t, x) = 0 $ in $ N(\geq 1) $ dimensions.
Keqiang Li, Shangjiu Wang
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Resonant problems for non-local elliptic operators with unbounded nonlinearites
Electronic Research Archive, 2023 In this paper we study the existence of nontrivial solutions of a class of asymptotically resonant problems driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions by applying Morse theory and critical groups ...
Yutong Chen, Jiabao Su
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Examples for the Infinite Dimensional Morse Lemma [PDF]
, 1983 Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped.
Buchner, Michael +2 more
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