Opuscula Math. 32, no. 3 (2012), 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

Ernest Yankson

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.

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• Ernest Yankson
• University of Cape Coast, Department of Mathematics and Statistics, Ghana
• Revised: 2011-12-31.
• Accepted: 2012-01-04.