Opuscula Math. 32, no. 3 (), 617-627
http://dx.doi.org/10.7494/OpMath.2012.32.3.617
Opuscula Mathematica

# Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay

Abstract. We use a variant of Krasnoselskii's fixed point theorem by T. A. Burton to show that the nonlinear neutral differential equation with functional delay $x'(t) = -a(t)h(x(t)) +c(t)x'(t-g(t)) + q(t,x(t) x(t-g(t)))$ has a periodic solution.
Keywords: fixed point, large contraction, periodic solution, totally nonlinear neutral equation.
Mathematics Subject Classification: 34K13, 34A34, 34K30, 34L30.