一类方程的李雅普诺夫函数的构造

Construction of Lyapunov Function of One Equation

用李雅普诺夫第二方法判断解的稳定性具有直接而简明的优点,但如何构造李雅普诺夫函数是一个难点。文章对于一类二阶常系数线性方程利用构造李雅普诺夫函数的方法,判断了其解的稳定性。

It is direct and concise to use Lyapunov second method to judge stability of solutions. But how to construct Lyapunov function is a difficulty. To one ordinary differential equation of second order with constant coefficients, we used method of construting Lyapunov function to judge the stability of solution.