摘要
目的研究一阶具有分段常数变量的脉冲微分方程的解的性质.方法单调迭代法、数学归纳法.结果对于一阶具有分段常数变量的脉冲微分方程m′(t)≤-Mm(t)-Nm([t-k]),m(ti+)≤bim(ti),这里,t∈J=[0,T]t≠tii=1,2,…,p.得到了不等式的解m(t)≤0的两个充分条件.结论一阶具有分段常数变量的脉冲微分方程的解m(t)在一定条件下满足m(t)≤0.
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.
出处
《河北北方学院学报（自然科学版）》
2008年第A03期1-3,共3页
Journal of Hebei North University:Natural Science Edition
关键词
分段常数变量
脉冲微分方程
单调迭代法
比较结果
piecewise constant arguments
impulsive differential equations
the monotonously iterative method
comparative results
