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

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-au(t))=p(t),quad tgeq0,; teq 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.

Keywords

• Second-order delay differential equations
• impulses
• periodic solution
• coincidence degree