A.M. Lyapunov proved inequality, which enables us to estimate distance between two consecutive zeros a and b of the solution of linear differential equation of the second order x″(t) + q(t)x(t) = 0, where q(t) is a continuous for t ∈ [a, b] function. In the present paper we solve analogous problem for the linear differential equation x″(t) + p(t)x′(t) + q(t)x(t) = 0. The obtained inequality is applicable for estimations of the periods of periodic solutions of non-linear differential equations such as A. Lienard and B. Van der Pol equations.

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关于Lyapunov型不等式

AM Lyapunov证明了不等式，这使我们能够估计二阶线性线性微分方程解x ''（t）+ q（t）x（t）= 0的两个连续零点a和b之间的距离，其中q（t）是连续为吨∈[ A，b ]的功能。在本论文中，我们求解线性微分方程类似问题X “（吨）+ p（吨）X '（吨）+ q（t）x（t）=0。获得的不等式适用于估计非线性微分方程（例如A. Lienard和B. Van der Pol方程）的周期解的周期。