| Title:
|
On the number of periodic solutions of a generalized pendulum equation (English) |
| Author:
|
Kubáček, Zbyněk |
| Author:
|
Rudolf, Boris |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
197-208 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
generalized pendulum |
| Keyword:
|
number of solutions |
| Keyword:
|
Jensen’s inequality |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1117.34041 |
| idMR:
|
MR2164670 |
| . |
| Date available:
|
2008-06-06T22:45:51Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107951 |
| . |
| Reference:
|
[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 |
| Reference:
|
[2] Markushevich, A. I.: Kratkij kurs teorii analitičeskich funkcij.Nauka Moskva 1978. (russian) MR 0542281 |
| Reference:
|
[3] Mawhin, J.: Points fixes, points critiques et probl‘emes aux limites.Sémin. Math. Sup. no. 92, Presses Univ. Montréal, Montréal 1985. MR 0789982 |
| Reference:
|
[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. |
| Reference:
|
[5] Ortega, R.: Counting periodic solutions of the forced pendulum equation.Nonlinear Analysis 42 (2000), 1055–1062. Zbl 0967.34037, MR 1780454 |
| Reference:
|
[6] Rachůnková, I.: Upper and lower solutions and topological degree.JMAA 234 (1999), 311–327. MR 1694813 |
| Reference:
|
[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. |
| . |
