Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T01:56:28.481Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on periodic solutions of some nonautonomous differential equations

Published online by Cambridge University Press:  17 April 2009

M. R. Grossinho  and
L. Sanchez
M. R. Grossinho
Affiliation:
C.M.A.F. and University of Lisbon, 2 Av. Prof. Gama Pinto, 1699 Lisboa Codex-Portugal.
L. Sanchez
Affiliation:
C.M.A.F. and University of Lisbon, 2 Av. Prof. Gama Pinto, 1699 Lisboa Codex-Portugal.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the existence of nontrivial periodic solutions of some nonlinear ordinary differential equations with time-dependent coefficients using variational methods.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 253 - 265
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Ambrosetti, A. and Rabinowitz, P.H., “Dual variational methods in critical point theory and applications”, J. Funct. Anal., 14 (1973), 349–381.CrossRefGoogle Scholar
[2]Austin, G., “Biomathemathematical model of aneurysm of the circle of willis, I: The Duffing equation and some approximate solutions”, Math. Biosci., 11 (1971), 163.CrossRefGoogle Scholar
[3]Bahri, A., Thèse de Doctorat d'État en Sciences Mathematiques, Université Pierre et Marie Curie, Paris.Google Scholar
[4]Cronin, J., “Biomathematical model of aneurysm of the circle of willis: A quantitative Analysis of the differential equation of Austin”, Math. Biosci., 16 (1973), 209–225.CrossRefGoogle Scholar
[5]Jacobowitz, H., “Periodic Solutions of x″ + f (x,t) = 0 via the Poincaré-Birkhoff Theorem”, J. Differential Equations, 20 (1976), 37–52.CrossRefGoogle Scholar
[6]Rabinowitz, P.H., “Free Vibrations for a semilinear wave equation”, Comm. Pure Appl. Math., 31 (1978), 31–68.CrossRefGoogle Scholar
[7]Rabinowitz, P.H., “Periodic Solutions of Hamiltonian systems”, Comm. Pure Appl. Math., 31 (1978), 157–184.CrossRefGoogle Scholar