Philos-type oscillation criteria for second-order linear impulsive differential equation with damping

Abstract

Abstract In this paper, the problem of oscillation for a second-order linear impulsive differential equation with damping is investigated. This equation can be more accurately used to model the states of many evolutionary processes, which are often subject to short-term perturbations and experience abrupt changes at certain moments of time. By employing a generalized Riccati transformation technique, we derive several oscillation criteria which are either new or improve several recent results in the literature. In addition, we provide an example to illustrate the effect of impulses on the oscillation of the equation.

Keywords

• Oscillation
• Impulse
• Riccati transformation
• Damping
• Integral averaging technique