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Multiple periodic solutions for perturbed relativistic pendulum systems


Authors: Petru Jebelean, Jean Mawhin and Călin Şerban
Journal: Proc. Amer. Math. Soc. 143 (2015), 3029-3039
MSC (2010): Primary 34C25; Secondary 35J25, 35J65
DOI: https://doi.org/10.1090/S0002-9939-2015-12542-7
Published electronically: February 16, 2015
MathSciNet review: 3336627
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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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Additional Information

Petru Jebelean
Affiliation: Department of Mathematics, West University of Timişoara, 4, Boulevard V. Pârvan 300223-Timişoara, Romania – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy
Email: jebelean@math.uvt.ro

Jean Mawhin
Affiliation: Research Institute in Mathematics and Physics, Université Catholique de Louvain, 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
Email: jean.mawhin@uclouvain.be

Călin Şerban
Affiliation: Department of Mathematics, West University of Timişoara, 4, Boulevard V. Pârvan 300223-Timişoara, Romania
Email: cserban2005@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12542-7
Received by editor(s): March 11, 2014
Published electronically: February 16, 2015
Additional Notes: The first and third authors’ support by grant PN-II-RU-TE-2011-3-0157 (CNCS-Romania) is gratefully acknowledged
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society