ABSTRACT
In this paper, we discuss the existence of extremal solutions for impulsive differential equations (IDE) with variable times using a new approach, develop the necessary comparison result parallel to the one in ODE and apply it for the investigation of stability criteria. In the context of stability investigation, it is natural to consider the existence of a solution that meets each given barrier (hypersurface) exactly once i.e., the lack of pulse phenomenon. With this motivation, we also consider a result on existence of solutions which meet the given hypersurfaces only once and this result is a refinement of the known result in [5]. We do hope that the new idea of this paper will be of value in the study of qualitative behavior of solutions of IDE with variable times whose progress so far has been slow.
