Interval oscillation criteria for forced mixed nonlinear impulsive differential equations with variable delay

Abstract In this paper, the interval qualitative properties of a class of mixed nonlinear impulsive differential equations are studied. Under the hypothesis of delay σ ( t ) being variable, the ratio of functions x ( t − σ ( t ) ) and x ( t ) on each considered interval is estimated, then Riccati transformation and \omega functions are applied to obtain interval oscillation criteria. The results gained by Ozbekler and Zafer (2011) for delay σ ( t ) = 0 and by Guo et al. (2012) for delay σ ( t ) being nonnegative constant are developed.