一类高阶微分方程组解的渐近行为(英文)

Asymptotic Behavior of the Solutions of a Class of High Order Differential Equations

对方程组Mx″+x′=f(t,x),x∈ΩRn,t∈R1,得到如下结果:若该方程组有一个解x1(t)满足limt→+∞x1(t,t0,x11,x12)=c,则存在方程组x′=f(t,x)的一解x2(t)=x2(t,t0,x20),使得limt→+∞‖x1(t,t0,x11,x12)-x2(t,t0,x20)‖=0.这一结果的某些推广和应用实例也在文中予以讨论.

It is proved that for any solution x1 （t） of the system Mx＂＋x＇=f（t, x）, in which lim x＇1 （t）=c, there exists a solution x2 （t） of the system x＇=f（t, x） such that lim ∥ x1（t; t0, x11, x12）-x2（t; t0, x2）∥=0. Furthermore, some generalizations of this result are also presented. Finally some examples are investigated explicitly.