International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 689-696
doi:10.1155/S0161171291000923
Oscillation criteria in neutral equations of n order with variable coefficients
Department of Mathematics, The University of Rhode Island, Kingston 02881-0816, RI, USA
Received 6 June 1990
Copyright © 1991 D. A. Georgiou and C. Qian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Consider the n-order neutral delay differential equation
dndtn[y(t)+P(t)y(t−τ)]+Q(t)y(t−σ)=0
where P,Q∈C[[t0,∞),ℝ] and the delays τ and σ are nonnegative real numbers. In this paper we
examined the oscillatory behavior of the solutions of the above equation using techniques which
allow the relaxation of the restrictions which has been introduced previously. We illustrate new
type of conditions which improve and extend known results, by relaxing hypotheses that P is
constant and Q is τ-periodic.