一类三维微分系统正值解的结构(英文)

The Structure of the Set of Nonoscillatory Solutions of Three-Dimensional Differential Systems

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.