Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 127, pp. 1-8.
Title: Existence of periodic solutions for neutral nonlinear
differential equations with variable delay
Authors: Deham Hafsia (Univ. of Annaba, Algeria)
Djoudi Ahcene (Univ. of Annaba, Algeria)
Abstract:
We use a variation of Krasnoselskii fixed point theorem
introduced by Burton to show that the nonlinear neutral differential
equation
$$
x'(t)=-a(t)x^3(t)+c(t)x'(t-g(t))+G(t,x^3(t-g(t))
$$
has a periodic solution. Since this equation is nonlinear,
the variation of parameters can not be applied directly;
we add and subtract a linear term to transform the
differential into an equivalent integral equation suitable
for applying a fixed point theorem. Our result is illustrated
with an example.
Submitted April 15, 2010. Published September 07, 2010.
Math Subject Classifications: 34K20, 45J05, 45D05.
Key Words: Periodic solution; nonlinear neutral differential equation;
large contraction; integral equation.