Existence of at least two periodic solutions of the forced relativistic pendulum
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- by Cristian Bereanu and Pedro J. Torres PDF
- Proc. Amer. Math. Soc. 140 (2012), 2713-2719 Request permission
Abstract:
Using Szulkin’s critical point theory, we prove that the relativistic forced pendulum with periodic boundary value conditions \begin{equation*} \left (\frac {u’}{\sqrt {1-u’^2}}\right )’ +\mu \sin u=h(t), \quad u(0)-u(T)=0=u’(0)-u’(T), \end{equation*} has at least two solutions not differing by a multiple of $2\pi$ for any continuous function $h:[0,T]\to \mathbb {R}$ with $\int _0^Th(t)dt=0$ and any $\mu \neq 0.$ The existence of at least one solution has been recently proved by Brezis and Mawhin.References
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Additional Information
- Cristian Bereanu
- Affiliation: Institute of Mathematics “Simion Stoilow”, Romanian Academy 21, Calea Griviţei, RO-010702 Bucharest, Sector 1, România
- Email: cristian.bereanu@imar.ro
- Pedro J. Torres
- Affiliation: Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
- MR Author ID: 610924
- ORCID: 0000-0002-1243-7440
- Email: ptorres@ugr.es
- Received by editor(s): December 15, 2010
- Received by editor(s) in revised form: March 2, 2011
- Published electronically: November 23, 2011
- Additional Notes: Support of the first author from the Romanian Ministry of Education, Research, and Innovation (PN II Program, CNCSIS code RP 3/2008) is gratefully acknowledged.
- Communicated by: Yingfei Yi
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2713-2719
- MSC (2010): Primary 34B15, 49J52, 49J35
- DOI: https://doi.org/10.1090/S0002-9939-2011-11101-8
- MathSciNet review: 2910759