Abstract:

In this paper,two kinds of stability theorems are improved.By the property of the Kfunction,the property of the function’s derivative in original Markin stability theorem is extended from the finite time to the infinite time,and this brings the new method to get the stability of the solution of the nonautonomous differential equation.By the supplement of the integral convergence theorem ,the new theorem is further improved and promoted,and a new determination method about uniform stability is obtained.

Key words: Malkin, Stability, Integral convergence, Uniform stability