Gronwall不等式的几个推广及其在微分方程中的应用

Some Generalized Gronwall's Inequalities andTheir Application in Diferential Equations

对经典的Gronwall不等式进行了推广,得到了Bihari型、带奇性型的Gronwall不等式和一种多维空间中Gronwall型不等式,并用实例说明了各种类型的Gronwall不等式在获得微分方程解的一些基本估计中的作用。

It is well-known that the inequality of Gronwalrs type may be important to estimate for the solutions of various differential equations. We intend to get some generalizations of this type of inequality such as Bihari＇s inequality, Gronwalrs inequality with singularity and Gronwall＇s inequality in several variables space. We also cite some examples in illustration of its application.