n维非自治系统周期解的个数  

THE NUMBER OF PERIODIC SOLUTION OF n-DIMENSIONAL NONAUTONOMOUS DIFFENTIAL SYSTEMS

作　　者：马荣国[1] 孙华荣[1] 

机构地区：[1]西安公路学院

出　　处：《青海师范大学学报（自然科学版）》1992年第1期17-21,共5页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：本文利用非线性泛函分析中拓扑度的理论,讨论了 n 维非自治系统x=A(t)x+1/λg(t,x).x∈R^n (1)并在系统(1)对应的齐次方程x=A(t)x x∈R^n (2)无非平凡周期解的情况下,得到系统(1)存在三个周期解的充分条件。ABSTRACT In this paper,We discuss the existence of periodic solution of n-dimensional system (?)=A(t)x+(1/λ)g(t,x) x∈R^n (1) and using the theory of topological degree,a sufficient condition in which the system (1) has at least three non-trival w-periodic solution is obtained,where homogeneous equation (?)=A(t)x x∈R^n (2) hasn't non-trival ω-periodic solution.

关 键 词：n维系统 拓扑度 周期解 齐次方程 

分 类 号：N55，G658.3[自然科学总论]