Periodic Solutions of Singular Lagrangian Systems

1993 ◽  
Author(s):  
Antonio Ambrosetti ◽  
Vittorio Coti Zelati
Keyword(s):  
Periodic Solutions ◽  
Lagrangian Systems

scholarly journals Stability from Index Estimates for Periodic Solutions of Lagrangian Systems

1994 ◽  
Vol 108 (1) ◽  
pp. 170-189 ◽  
Author(s):  
G. Dellantonio ◽  
B. Donofrrio ◽  
I. Ekeland
Keyword(s):  
Periodic Solutions ◽  
Lagrangian Systems

Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results

1998 ◽  
Vol 50 (3) ◽  
pp. 497-524
Author(s):  
Philippe Bolle
Keyword(s):  
Periodic Solutions ◽  
Critical Points ◽  
Morse Index ◽  
Approximate Solutions ◽  
Existence Results ◽  
Lagrangian Systems ◽  
Potential Well ◽  
Regular Solutions ◽  
Open Set

AbstractThis paper deals with periodic solutions for the billiard problem in a bounded open set of ℝN which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.

INFINITELY MANY EVEN PERIODIC SOLUTIONS OF LAGRANGIAN SYSTEMS ON ANY RIEMANNIAN TORI WITH EVEN POTENTIAL IN TIME

2009 ◽  
Vol 11 (02) ◽  
pp. 309-335 ◽  
Author(s):  
GUANGCUN LU ◽  
MINGYAN WANG
Keyword(s):  
Periodic Solutions ◽  
Periodic Potential ◽  
Lagrangian System ◽  
Lagrangian Systems ◽  
Integer Multiple ◽  
Smooth Potential

In this paper, we prove that the Lagrangian system on any Riemannian torus with C3-smooth even and τ-periodic potential in time possesses infinitely many different periodic contractible even solutions with integer multiple periods of τ. As a consequence, we get that the same conclusion holds for any τ > 0 and the Lagrangian system on any Riemannian torus with C3-smooth potential independent of time.

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