Interval oscillation criteria for nonlinear impulsive differential equations with variable delay

In this paper, the interval qualitative properties of a class of second order nonlinear differential equations are studied. For the hypothesis of delay being variable iota(t), an "interval delay function" is introduced to estimate the ratio of functions x(t - iota(t)) and x(t) on each considered interval, then Riccati transformation and H functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng [Comput. Math. Appl. 59(2010), 18-30] under the assumption of constant delay t are developed. Moreover, examples are also given to illustrate the effectiveness and non-emptiness of our results.