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Keywords:
generalized pendulum; number of solutions; Jensen’s inequality
generalized pendulum; number of solutions; Jensen’s inequality
Summary:
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.
References:
[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 1382058
[2] Markushevich, A. I.: Kratkij kurs teorii analitičeskich funkcij. Nauka Moskva 1978. (russian) MR 0542281
[3] Mawhin, J.: Points fixes, points critiques et probl‘emes aux limites. Sémin. Math. Sup. no. 92, Presses Univ. Montréal, Montréal 1985. MR 0789982
[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 1780454 | Zbl 0967.34037
[6] Rachůnková, I.: Upper and lower solutions and topological degree. JMAA 234 (1999), 311–327. MR 1694813
[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.
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