A simple variational approach to a converse of the Lagrange-Dirichlet theorem
type: Item
instance of: scholarly article
title: A simple variational approach to a converse of the Lagrange-Dirichlet theorem
zbMATH Open document ID: 0781.70015
DOI: 10.1007/BF00380318
author: Peter Hagedorn
author: Jean Mawhin
published in: Archive for Rational Mechanics and Analysis
publication date: 1993-09-07T00:00:00Z
review text: The Lagrange-Dirichlet stability theorem is reformulated. In the setting of a Hilbert space the proof is made possible by the fact that the functional to be varied is strictly coercive.
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70H30
zbMATH DE Number: 410086
zbMATH Keywords: coercive functional
zbMATH Keywords: Hilbert space
reviewed by: Johannes Viktor Feitzinger
MaRDI profile type: Publication
cites work: On instability of the position of equilibrium of a Hamiltonian system
cites work: Asymptotic solutions of equations of dynamics
cites work: On the asymptotic solutions of the equations of motion of mechanical systems
cites work: Die Umkehrung der Stabilitätssätze von Lagrange-Dirichlet und Routh. (The inversion of the stability theorems of Lagrange-Dirichlet and Routh.)
cites work: Eine zusätzliche Bemerkung zu meiner Arbeit: ''Die Umkehrung der Stabilitätssätze von Lagrange-Dirichlet und Routh''
cites work: Q4403774
cites work: Instability of equilibrium in a potential field
cites work: On the instability of equilibrium in a potential field
cites work: Asymptotic solutions of equations of classical mechanics
cites work: Calculus of variations in the large and classical mechanics
cites work: Asymptotic motions and the inversion of the Lagrange-Dirichlet theorem
cites work: Q4741745
cites work: On the inversion of the Lagrange-Dirichlet theorem in the case of an analytic potential
cites work: Q3858615
cites work: On the instability of equilibrium when the potential has a non-strict local minimum
cites work: On instability of equilibrium when the force function is not a maximum
cites work: Critical point theory and Hamiltonian systems
cites work: On the inversion of the Lagrange-Dirichlet theorem in a case of nonhomogeneous potential
cites work: On the inversion of Lagrange-Dirichlet theorem
cites work: Stability of equilibrium in a potential field
cites work: An example of non isolated equilibrium with maximum potential, stabilized by dissipative forces
cites work: Stability theory by Liapunov's direct method
cites work: On the inversion of the Lagrange-Dirichlet stability theorem mechanical and generalized systems
cites work: An inversion of the Lagrange-Dirichlet stability theorem
cites work: Instability of an equilibrium in a potential field
cites work: Analytical mini-max methods for Hamiltonian brake orbits of prescribed energy
cites work: Q3706544
cites work: Inversion of Lagrange's theorem for a rigid body with a cavity containing a viscous liquid
description: scientific article; zbMATH DE number 410086