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.