A global solution curve for a class of periodic problems, including the relativistic pendulum

Abstract

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of periodic solutions. Our approach is suitable for numerical computations, and in fact we present some numerically computed bifurcation diagrams illustrating our results.

Keywords:

• periodic solutions
• the relativistic pendulum equation
• numerical computations of bifurcation diagrams

AMS Subject Classifications:

• 34C25
• 65L10
• 83C10

Acknowledgements

This work was supported by the grants of RFBR No 10-04-00913, Federal goal-oriented program No 02.740.11.0700 and the Black Stones hunting enterprise.