Comparative Results of First Order Impulsive Differential Equations with Piecewise Constant Arguments

Objective To investigate characters of the solution to first order impulsive differential equations with piecewise constant arguments.Method The monotonously iterative method and the mathematical induction.Resutlt Two sufficient conditions of the solution m(t)≤0 for first order impulsive differential equations with piecewise constant arguments——m′(t)≤-M(m)t-Nm(),m(t+i)≤bim(ti),where t∈J=t≠ti i=1,2,…,p,are obtained.Conclusion The solution m(t) to first order impulsive differential equations with piecewise constant arguments satisfies m(t)≤0 under certain conditions.