一类三维微分系统正值解的结构

摘要

研究三维微分系统：u′1=a1（t）｜u2｜λ1sgn u2,u′2=a2（t）｜u3｜λ2sgn u3,u′3=-a3（t）｜u1｜λ3sgn u1.假设λi（i=1,2,3）是正的常数,ai（t）（i=1,2,3）在区间[0,∞）上是正的连续函数,根据u的分量ui的特殊渐近条件定义了正值解的几种类型。系统满足条件∫0∞ai（t）dt=∞,i=1,2.%The three-dimensional differential system u′1=a1（t）｜u2｜λ1sgn u2,u′2=a2（t）｜u3｜λ2sgn u3,u′3=-a3（t）｜u1｜λ3sgn u is considered under the assumptions that λ i （ i = 1,2,3） are positive constants andai（t） （i = 1,2,3） are positive continuous functions on [0,∞）,and several classes of nonoscillatory solutions u of （S） having specific asymptotic growths as t -＋ Go are established. The system satisfies ∫0∞ai（t）dt=∞,i=1,2.