Existence and Uniqueness of Periodic Solutions for (2k)th-Order Delay Differential Equations

Article Preview

Abstract:

The existence of periodic solutions for a class of even order delay differential equations is obtained. It is useful in the delay problem of wireless beaconage. The proofs are based on combining a method of Fourier analysis with Schauder fixed point theorem. This generalizes results developed by W. Layton to high order equations

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 538-541)

Pages:

2500-2503

Citation:

Online since:

June 2012

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] F. Z. Cong, Periodic solutions for 2kth with ordinary differential equations with non resonance, Nonlinear Anal. 32 (1997),787-793.

DOI: 10.1016/s0362-546x(97)00517-8

Google Scholar

[2] F. Z. Cong, Q. D. Huang and S. Y. Shi, Existence and uniqueness of periodic solutions for (2n+1)th-order differential equations, J.Math. Anal. Appl. 241(2000), 1-9.

Google Scholar

[3] W. Layton, Periodic solutions of nonlinear delay equations, J.Math. Anal. Appl. 77,(1980), 198-204.

Google Scholar

[4] A. C. Lazer, Application of lemma on bilinear forms to a problem in nonlinear oscillations, Proceedings of the American Mathematical Society. 33 (1972), 89-94.

DOI: 10.1090/s0002-9939-1972-0293179-9

Google Scholar

[5] W. Li, Periodic solutions for $2k$th order ordinary differential equation with resonance, J. Math. Anal. Appl. 259 (2001),157-167.

Google Scholar

[6] Y. Li and H. Z. Wang, Periodic solutions of high order Duffing equations, Appl. Math. Chinese Univ. 6 (1991), 407-412.

Google Scholar

[7] B. G. Liu and L. H. Huang, Periodic solutions for nonlinear n th order differential equations with delays, J. Math. Anal. Appl. 313 (2006), 700-716.

Google Scholar

[8] R. Iannacci and M. N. Nkashama, On periodic solutions of forced second order differential equations with deviating arguments, Lecture Notes in Mathematical. 1151 (1984), Springer-Verlag, 224-232.

DOI: 10.1007/bfb0074731

Google Scholar

[9] Krasnosel'skll. M. A., Topological methods in the theory of nonlinear integral equations, Macmillan Co., (1964), NewYork.

Google Scholar

[10] S. Lu and W. Ge, Periodic solutions for a kind of Lie nard equations with deviating arguments, J. Math.Anal. Appl. 249 (2004), 213-243..

Google Scholar