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.

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  • 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.
Opuscula Mathematica - cover

Cite this article as:
Emmanuel K. Essel, Ernest Yankson, On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay, Opuscula Math. 34, no. 3 (2014), 469-481, http://dx.doi.org/10.7494/OpMath.2014.34.3.469

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