In this paper, We give the sufficient conditions of the unstability of zero solution for the third order linear differential equation with periodic coefficients d^3x/dt^3+A(t)dx/dt+B(t)x=0.
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In this paper, We give the sufficient conditions of the unstability of zero solution for the third order linear differential equation with periodic coefficients d^3x/dt^3+A(t)dx/dt+B(t)x=0.
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.
