Electron. J. Diff. Equ., Vol. 2011 (2011), No. 37, pp. 1-12.

Existence of periodic solutions for second order delay differential equations with impulses

Lijun Pan

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 3, 2011.
Math Subject Classifications: 34K13, 34K45.
Key Words: Second-order delay differential equations; impulses; periodic solution; coincidence degree.

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Lijun Pan
School of Mathematics, Jia Ying University
Meizhou Guangdong, 514015, China
email: plj1977@126.com

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