Leighton and Wong type oscillation theorems for impulsive differential equations

Abstract

We obtain the well-known Leighton and Wong oscillation theorems for a general class of second-order linear impulsive differential equations by making use of the recently established results on the existence of nonprincipal solutions. The results indicate that the oscillation character of solutions may be altered by the impulsive perturbations, which is not the case in most published works. Another difference is that the equations are quite general in the sense that the impulses are allowed to appear on both solutions and their derivatives. Examples are also given to illustrate the importance of the results. (C) 2021 Elsevier Ltd. All rights reserved.