Title: Oscillation results for higher order nonlinear neutral differential equations

Authors: Saroj Panigrahi; Rakhee Basu

Addresses: School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India ' School of Mathematics and Statistics, University of Hyderabad, Hyderabad-500 046, India

Abstract: In this paper, the authors investigated the oscillatory and asymptotic behaviour of solution of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. We have established a new conditions which guarantees that every solutions either oscillatory or converges to zero. Moreover, using Schauder's fixed point theorem sufficient conditions are obtained for the bounded positive solutions. Examples are considered to illustrate the main results.

Keywords: functional differential equations; neutral differential equations; nonlinear differential equations; oscillation; positive coefficients; negative coefficients; oscillatory behaviour; asymptotic behaviour; fixed point theorem.

DOI: 10.1504/IJDSDE.2016.074573

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.1, pp.16 - 35

Received: 24 Sep 2014
Accepted: 18 Apr 2015
Published online: 06 Feb 2016 *

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