Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 37, pp. 1-12.
Title: Existence of periodic solutions for second order delay
differential equations with impulses
Author: Lijun Pan (Jia Ying Univ., Meizhou, China)
Abstract:
Using the coincidence degree theory by Mawhin,
we prove the existence of periodic solutions for the
second-order delay differential equations with impulses
$\displaylines{
x''(t)+f(t,x'(t))+g(x(t-\tau(t))=p(t),\quad t\geq0,\; t\neq t_k,\cr
\Delta x(t_k)=I_k(x(t_k),x'(t_k)),\cr
\Delta x'(t_k)=J_k(x(t_k),x'(t_k)).
}$$
We obtain new existence results and illustrated them by an example.
Submitted January 28, 2011. Published March 03, 2011.
Math Subject Classifications: 34K13, 34K45.
Key Words: Second-order delay differential equations; impulses;
periodic solution; coincidence degree.