一阶向量微分方程的微分不等式技巧

The differential inequalities technique of the first order vector differential equations

利用上、下解方法,研究一阶向量微分方程初值的解的存在性与解的估计问题;同时,将所得结果应用于n阶微分方程的初值问题,获得了n阶微分方程的初值问题解的存在性及估计.

Using the method of the upper and lower solutions, the existence and estimate of solutions of the initial value problem for first-order vector differential equations is studied. The main result is then applied to the initial value problem for n-order differential equations and some related results are obtained.