On the number of periodic solutions of a generalized pendulum equation
Archivum mathematicum, Tome 41 (2005) no. 2, pp. 197-208 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For a generalized pendulum equation we estimate the number of periodic solutions from below using lower and upper solutions and from above using a complex equation and Jensen’s inequality.
For a generalized pendulum equation we estimate the number of periodic solutions from below using lower and upper solutions and from above using a complex equation and Jensen’s inequality.
Classification : 34B15, 34C25, 47N20
Keywords: generalized pendulum; number of solutions; Jensen’s inequality
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Kubáček, Zbyněk; Rudolf, Boris. On the number of periodic solutions of a generalized pendulum equation. Archivum mathematicum, Tome 41 (2005) no. 2, pp. 197-208. http://geodesic.mathdoc.fr/item/ARM_2005_41_2_a8/

[1] Il’yashenko, Y., Yakovenko, S.: Counting real zeros of analytic functions satisfying linear ordinary differential equations. J. Differential Equations 126 (1996), 87–105. | MR

[2] Markushevich, A. I.: Kratkij kurs teorii analitičeskich funkcij. Nauka Moskva 1978. (russian) | MR

[3] Mawhin, J.: Points fixes, points critiques et probl‘emes aux limites. Sémin. Math. Sup. no. 92, Presses Univ. Montréal, Montréal 1985. | MR

[4] Mawhin, J.: Seventy-five years of global analysis around the forced pendulum equation. Proceedings of the Conference Equadiff 9 (Brno, 1997), Masaryk Univ. 1998, pp. 861–876.

[5] Ortega, R.: Counting periodic solutions of the forced pendulum equation. Nonlinear Analysis 42 (2000), 1055–1062. | MR | Zbl

[6] Rachůnková, I.: Upper and lower solutions and topological degree. JMAA 234 (1999), 311–327. | MR

[7] Rudolf, B.: A multiplicity result for a generalized pendulum equation. Proceedings of the 4$^{\text{th}}$ Workshop on Functional Analysis and its Applications, Nemecká 2003, 53–57.