多元Volterra线性积分不等式组及其对线性微分系统的应用

Linear System of Volterra Integral Inequalities in Several Variables and Its Application to Linear Differential Systems

在核函数不具备文献中常见的任何附加假设的情况下，对ｎ元Ｖｏｌｔｅｒｒａ线性积分不等式的一般形组，获得一切连续解的显式逐点界值公式．作为应用，对一般形线性微分方程组建立了解的先验界值公式，它在线性齐次微分方程情形中的推论，与周知的Ｗａｚｅｗｓｋｉ，Ｂｕｔｌｅｗｓｋｉ的界值公式是相互独立不可比较的，同时还讨论了某些不同而又互相联系的线性微分系统初值问题的解的偏差估计问题．

A prior explicit bound for continuous solutions to general linear system of Volterra -type integral inequalities in several variables is obtained, without assumptions on kernel functions as usually required by authors.Our result will have a wider range of application than those proved in the references[1-7]. As application of the result obtained,a prior bound on solutions to the general linear inhomogenerous differential system is derived,which is incomparable with the well-known results of Wazewski and Butlewski established only for linear homogeneous differential systems.Some further applications are also induded.