Philos-type oscillation criteria for linear differential equations with impulsive effects

Abstract

Abstract The present paper deals with the problem of oscillation for a second-order linear differential equation in which an impulsive effect is considered. This equation can be regarded as an equation of motion in which the moving speed of a mass point changes sharply by some influence. It is proved that there is a case that the mass point may oscillate due to the influence of the impulsive effect even if the mass point does not oscillate in the model removing the impulsive effect. It is also shown that the obtained results extend some previous ones through the use of an example.