Oscillation criteria for a linear neutral differential equation

For a neutral differential equation ˙x(t)− a(t) ˙x g(t) + b(t )x h(t) = 0, 0 a(t)< 1, b(t) 0, g(t) t, h(t) t, a connection between oscillation properties of the differential equation and differential inequalities is established. Explicit nonoscillation and oscillation conditions and a comparison theorem are presented.  2003 Elsevier Inc. All rights reserved. 1. Introduction