周期系数线性系的若干性质

The properties of periodic linear coefficient

周期系数二阶线性方程x″+p(t)x′+q(t)x=0,其特征根实部为负不能保证渐进稳定性,因此与常系数二阶线性系有重大差别.但二者也有不少相同或相近之处.本文讨论当p(t),q(t)满足各种条件时,方程x″+p(t)x′+q(t)x=0的特征指数的特性,并指出其与常系数二阶线性系的性质异同.

Periodic second-order equation x″＋p（t）x＇＋q（t）x=0,the real parts of characteristic roots are neggative so that it cannot make sure the asymptotic stability.Therefore,there are big differences from constant second-order system.However,if analyzed carefully,there are quite a lot same or similar parts.This differences and similarities between them is discussed in this paper.This paper analyzes the characteristic exponents of the equation x″＋p（t）x＇＋q（t）x=0 with different p（t）and q（t）.