Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type

Abstract

We examine scalar differential equations with general piecewise constant arguments of mixed type, in short DEPCAG of mixed type, that is, the arguments are general step functions. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.