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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