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

Using the coincidence degree theory by Mawhin, we prove the existence of periodic solutions for the second-order delay differential equations with impulses
  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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