Gronwall不等式的证明及有关应用

Proofs and Applications of Gronwall Inequality

在证明Gronwall不等式的基础上,应用Gronwall不等式来证明存在唯一性定理中的唯一性、解的不等式、特殊的初值问题的解的存在性,以及有关微分方程及摄动方程的解的渐近性质。

First,this paper provides two proofs of Gronwall inequality. Then,we apply it to prove the uniqueness of the existence and uniqueness theorem,the inequality of the solution and the existence of the solution to special initial value problem. At last,we apply it to prove the theorem about the asympototic property of the solution to the differential and perturbed equation.