International Journal of Mathematics and Mathematical Sciences 
Volume 17 (1994), Issue 2, Pages 361-368
doi:10.1155/S0161171294000505

Oscillation in neutral equations with an “integrally small” coefficient

J. S. Yu1 and Ming-Po Chen2

 1Department of Applied Mathematics, Hunan University, Hunan, Changsha 410082, China
2Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan
Received 17 March 1992; Revised 14 September 1992

Abstract

Consider the neutral delay differential equationddt[x(t)−P(t)x(t−τ)]+Q(t)x(t−δ)=0,   t≥t0        (*)Where P, Q∈C([t0,∞],R+), τ∈(0,∞) and δ∈R+. We obtain several sufficient conditions for the oscillation of all solutions of Eq. (*) without the restriction ∫t0∞Q(s)ds=∞.