IJPAM: Volume 55, No. 3 (2009)

EXISTENCE OF PERIODIC SOLUTIONS FOR $n$-TH
ORDER DIFFERENTIAL EQUATIONS WITH
DEVIATING ARGUMENT

Xing Rong Chen$^1$, Li Jun Pan$^2$
$^{1,2}$Department of Mathematics
Jia Ying University
Meizhou, Guangdong, 514015, P.R. CHINA
$^1$e-mail: cxrgd@tom.com
$^2$e-mail: plj1977@126.com


Abstract.By employing the coincidence degree theory of Mawhin, we study the existence of periodic solutions for $n$-th order differential equations with deviating argument $x^{(n)}(t)+\sum\limits^{n-1}_{i=2}b_{i}x^{(i)}(t)+f(x(t))x^{'}(t)+
g(t,x(t),x(t-\tau(t)))=p(t)$. Some new results on the existence of periodic solutions of the equations are obtained. Our work generalizes the known results.

Received: June 4, 2008

AMS Subject Classification: 34K13

Key Words and Phrases: $n$-th order differential equations, deviating argument, periodic solution, coincidence degree

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3