Opuscula Math. 34, no. 3 (2014), 469-481
http://dx.doi.org/10.7494/OpMath.2014.34.3.469
Opuscula Mathematica
On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay
Emmanuel K. Essel
Ernest Yankson
Abstract. We prove that the totally nonlinear second-order neutral differential equation \[\frac{d^2}{dt^2}x(t)+p(t)\frac{d}{dt}x(t)+q(t)h(x(t))\] \[=\frac{d}{dt}c(t,x(t-\tau(t)))+f(t,\rho(x(t)),g(x(t-\tau(t))))\] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.
Keywords: Krasnoselskii, neutral, positive periodic solution.
Mathematics Subject Classification: 34K20, 45J05, 45D05.
- Emmanuel K. Essel
- University of Cape Coast, Department of Mathematics and Statistics, Cape Coast, Ghana
- Ernest Yankson
- University of Cape Coast, Department of Mathematics and Statistics, Cape Coast, Ghana
- Received: 2013-05-23.
- Revised: 2014-02-07.
- Accepted: 2014-02-14.
