International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 689-696

Oscillation criteria in neutral equations of n order with variable coefficients

D. A. Georgiou and C. Qian

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.


Consider the n-order neutral delay differential equation dndtn[y(t)+P(t)y(tτ)]+Q(t)y(tσ)=0 where P,QC[[t0,),] 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.