多比例延迟微分方程精确解的性质

摘要

The structure of exact solution set of multi pantograph delay differential equation is studied and existence and uniqueness of an exact solution is proved. Dirichlet series solutions are coustructed to study the sufficient condition of the asymptotic stability of solution. By using technique that embed pantograph delay differential equation into infinite dimension ordinary differential equation, the conditions to guarantee the dissipation of solution and a numerical method adaptable for parallel computer are obtained.%研究了多比例延迟微分方程y(t)=ay(t)+by(q1t)+cy(q2t)的精确解的结构，探讨了初值问题解的唯一性和存在性.构造了Dirichlet级数解，据此给出精确解渐近稳定的充分条件.此外将延迟微分方程嵌入无限维常微分方程组中，给出了精确解稳定的条件，并由此得到一种适合于并行机的计算方法.