Consider the secnod order linear differential system with periodic coefficients x=A(t)x (*) and the stability problem of its trivial solution. In this paper, there are several conditions which are given including a ne...Consider the secnod order linear differential system with periodic coefficients x=A(t)x (*) and the stability problem of its trivial solution. In this paper, there are several conditions which are given including a necessary and sufficient condition for asymptotic stability, a necessary and sufficient condition for some kind of unstability, and a sufficient condition for stability. These conditions are expressed directly by coefficients A(t) instead of eharacteristie values of the system (*). Therefore, a feasible method of judging stability of the system (*) is offered.展开更多
文摘Consider the secnod order linear differential system with periodic coefficients x=A(t)x (*) and the stability problem of its trivial solution. In this paper, there are several conditions which are given including a necessary and sufficient condition for asymptotic stability, a necessary and sufficient condition for some kind of unstability, and a sufficient condition for stability. These conditions are expressed directly by coefficients A(t) instead of eharacteristie values of the system (*). Therefore, a feasible method of judging stability of the system (*) is offered.
