Interval oscillation criteria for nonlinear differential equations with impulses and 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 tau(t) being variable, the definitions of "strong zero point" and "weak zero point" are introduced and their effects on the estimation of function x(t - tau(t))/x(t) on each considered interval are investigated, then Riccati transformation and omega functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng (2010) for tau(t) being constant and by Zhou and Wang (2016) for tau(t) being variable are developed. (C) 2018 Elsevier Ltd. All rights reserved.