一类微分不等式与半线性微分方程

ONE CLASS OF DIFFERENTIAL INEQUALITIES AND SEMILINEAR DIFFERENTIAL EQUATIONS

给出了一类二阶线性Gronwall不等式的初等证明 ,并应用到非线性Newton运动方程的初值和边值问题中 。

One class of second order linear Gronwall inequalities is proved by the elementary methods. The inequalities are applied to the initial value problems and boundary value problems of nonlinear differential equations.The errors among the solutions to differential equations are analyzed with practice examples. The curves of solutions of differential equations and their graphs are given.