Oscillatory and Periodic Solutions of Impulsive Differential Equations with Piecewise Constant Argument

Abstract

We study the existence of oscillatory and periodic solutions of a class of first order scalar impulsive delay differential equations with piecewise constant argument.

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

“…The study of the existence of oscillatory and periodic solutions is one of the most interesting topics for applications. The oscillatory and periodic solutions with deviating arguments has been the subject of many investigations; see, for instance, [1,2,6,7,10,12,14,16,18,21,22,[30][31][32]34] and the references cited therein. Of particular importance, however, has been the study of oscillatory and periodic solutions which are caused by the argument deviations and which do not appear in the corresponding ordinary differential equations; see [23].…”

Asymptotical stability of Runge–Kutta methods for advanced linear impulsive differential equations with piecewise constant arguments

“…On the other hand, it is well known that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics do exist impulsive effects [10]. Recently, the existence, uniqueness and oscillation of the exact solutions of impulsive differential equations with piecewise constant arguments have been widely studied [3,4,[8][9][10]. But many impulsive differential equations with piecewise constant arguments can not be solved exactly or the solving is complicated.…”

Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

“…There are also some papers of the authors: In [9], the oscillatory and periodic solutions of the first order linear scalar impulsive delay differential equation and in [4], existence and uniqueness and also oscillatory and periodic solutions of a class of first order nonhomogeneous advanced impulsive differential equations with piecewise constant arguments were studied. The asymptotic convergence of first order delay and advanced impulsive differential equations with piecewise constant arguments were also considered in [2], [3] and [14].…”