Interval oscillation criteria for nonlinear impulsive differential equations with variable delay

Xiaoliang Zhou, Wu-Sheng Wang
2016 Electronic Journal of Qualitative Theory of Differential Equations  
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 τ(t), an "interval delay function" is introduced to estimate the ratio of functions x(t − τ(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
more » ... nder the assumption of constant delay τ are developed. Moreover, examples are also given to illustrate the effectiveness and non-emptiness of our results.
doi:10.14232/ejqtde.2016.1.101 fatcat:kac357ooyfdylktyqvmugslqte