A simple proof of multiplicity for periodic solutions of Lagrangian difference systems with relativistic operator and periodic potential

2015 ◽  
Vol 22 (2) ◽  
pp. 306-315 ◽  
Author(s):  
J. Mawhin
Keyword(s):  
Periodic Solutions ◽  
Simple Proof ◽  
Periodic Potential ◽  
Difference Systems

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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