Interval oscillation criteria for nonlinear differential equations with impulses and variable delay (Q1992228)

This paper deals with the second order impulsive delay differential equation of the form \[ x^{\prime\prime}(t)+p(t)g(x(t-\tau (t))) =f(t),~t\geq t_{0},~t\neq \theta _{k}, \] \[ x(t^{+}) =a_{k}x(t),~x^{\prime }(t^{+})=b_{k}x^{\prime }(t_{k}),~t=\theta _{k},~k=1,2,\dots . \] First, strong zero point and weak zero point are defined. Then an estimation for the function \(x(t-\tau (t))/x(t)\) is obtained. Finally, using the Riccati transformation, some interval oscillation criteria are established.