Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Periodic Solutions for a Higher Order Nonlinear Neutral Functional Differential Equation

Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335314

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 895

References:


[1] R. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.
[2] J. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977.
[3] W. Layton, Periodic solutions of a nonlinear delay equations, J.Math.Anal.Appl. 77(1980)198-204.
[4] S. Ma, Z. Wang, J. Yu, An abstract theorem at resonance and its applications, J.Diffential Equations. 145(1998)274-294.
[5] X. Huang, Z. Xiang, On the existence of 2¤Ç-periodic solutions of Duffing type equation x(t) + (g(t, x(t − ¤ä)) = p(t), Chinese Sci. Bull. 39(1994)201-203.
[6] S. Lu, W. Ge, Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument, Nonlinear Anal. 56(2004)501-514.
[7] J. Gossez, P. Omari, Periodic solutions of a second order ordinary equation: a necessary and sufficient condition for non- resonance, J.Differential Equations 94(1991)67-82.
[8] S. Lu, On the existence of positive solutions for neutral functional differential equation with multiple deviating arguments, J.Math.Anal.Appl. 280(2003)321-333.
[9] K. Wang , S. Lu, On the existence of periodic solutions for a kind of high-order neutral functional differential equation, J.Math.Anal.Appl. 326(2007)1161-1173.
[10] S. Lu, W. Ge, On the existence of periodic solutions for a kind of second order neutral functional differential equation, Acta.Math.Sini. 21(2005)381-392.
[11] S. Lu, W. Ge, Z. Zheng, Periodic solutions for a kind of Rayleigh equation with a deviating argument, Appl.Math.Lett. 17(2004)443-449.
[12] X. Yang, An existence result of periodic solutions, Appl.Math.Comput. 123(2001)413-419.