Interval oscillation criteria for nonlinear differential equations with impulses and variable delay

Abstract In this paper, the interval qualitative properties of a class of second order nonlinear differential equations are studied. For the hypothesis of delay τ ( 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 − τ ( t ) ) ∕ x ( t ) on each considered interval are investigated, then Riccati transformation and ω functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng (2010) for τ ( t ) being constant and by Zhou and Wang (2016) for τ ( t ) being variable are developed.