Geodesic
Existence of periodic solutions for second order delay differential equations with impulses
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 34K13, 34K45
Keywords: second-order delay differential equations, impulses, periodic solution, coincidence degree 
@article{EJDE_2011__2011__a57,
     author = {Pan,  Lijun},
     title = {Existence of periodic solutions for second order delay differential equations with impulses},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1216.34078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a57/}
}
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AU  - Pan,  Lijun
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JO  - Electronic journal of differential equations
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%T Existence of periodic solutions for second order delay differential equations with impulses
%J Electronic journal of differential equations
%D 2011
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%F EJDE_2011__2011__a57
Pan,  Lijun. Existence of periodic solutions for second order delay differential equations with impulses. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a57/