Multiple periodic solutions for perturbed relativistic pendulum systems

Jebelean, Petru; Mawhin, Jean; Şerban, Călin

doi:10.1090/S0002-9939-2015-12542-7

Multiple periodic solutions for perturbed relativistic pendulum systems
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by Petru Jebelean, Jean Mawhin and Călin Şerban

Proc. Amer. Math. Soc. 143 (2015), 3029-3039

DOI: https://doi.org/10.1090/S0002-9939-2015-12542-7

Published electronically: February 16, 2015

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Abstract:

We show that the periodically perturbed $N$-dimensional relativistic pendulum equation has at least $N+1$ geometrically distinct periodic solutions. Also, we obtain the existence of infinitely many solutions for systems with oscillating potential. Both results are obtained by reduction to an equivalent non-singular problem using classical critical point theory.

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