Opuscula Math. 32, no. 3 (2012), 617-627
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.
- Received: 2011-11-09.
- Revised: 2011-12-31.
- Accepted: 2012-01-04.