Geodesic
Periodic solutions for neutral nonlinear differential equations with functional delay
Electronic journal of differential equations, Tome 2003 (2003)
We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with functional delay

$ x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q\big(t, x(t), x(t-g(t)\big) $

has a periodic solution. Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique.
Classification : 34K20, 45J05, 45D05
Keywords: Krasnoselskii, neutral, nonlinear, integral equation, periodic solution, unique solution 
@article{EJDE_2003__2003__a3,
     author = {Raffoul,  Youssef N.},
     title = {Periodic solutions for neutral nonlinear differential equations with functional delay},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1054.34115},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a3/}
}
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JO  - Electronic journal of differential equations
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%A Raffoul,  Youssef N.
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Raffoul,  Youssef N. Periodic solutions for neutral nonlinear differential equations with functional delay. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a3/