Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T03:22:12.859Z Has data issue: false hasContentIssue false
  • English
  • Français

Floquet solutions of non-linear ordinary differential equations

Published online by Cambridge University Press:  14 November 2011

H. S. Hassan
H. S. Hassan
Affiliation:
Department of Mathematics, University of Qatar, P.O. Box 2713, Doha, Qatar
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we study the solutions of the boundary value problem

where t ∊ℝ, x ∊ ℝN, f is a continuous function of (t,x)and locally Lipschitz in x and ω is a fixed positive number and λ ∊ ℝ. By using degree theory we prove results on the existence of solutions of (*) and the dependence of such solutions on λ. We shall prove that (*) does not have an isolated solution, and study the topological properties of the components of solutions of (*).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 267 - 275
Copyright
Copyright © Royal Society of Edinburgh 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bebernes, J. W.. A simple alternative problem for finding periodic solutions of second order differential systems. Proc. Amer. Math. Soc. 42 (1974), 121–127.CrossRefGoogle Scholar
2Hartman, P.. Ordinary Differential Equations (New York: John Wiley, 1964).Google Scholar
3Hurewicz, W.. Lectures on ordinary Differential Equations (New York: M.I.T. Press and John Wiley, 1958).CrossRefGoogle Scholar
4Kotin, L.. A Floquet theorem for real non-linear systems. J. Math. Anal. Appl. 21 (1968), 384–388.CrossRefGoogle Scholar
5Lloyd, N. G.. Degree Theory. Cambridge Tracts in Mathematics 73 (Edinburgh: Cambridge University Press, 1978).Google Scholar
6Schmitt, K.. Periodic solutions of small period systems of nth order differential equations. Proc. Amer. Math. Soc 36 (1972), 459–463.Google Scholar