【摘要】 研究三维微分系统:{u′1=a1(t)|u2|λ1sgnu2u′2=a2(t)|u3|λ2sgnu3u′3=-a3(t)|u1|λ3sgnu1(S)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(ui(t)>0(i=1,3),u2(t)<0))的特殊渐近条件,应用Schauder-Tyehnoff不动点定理给出了一种特殊类型非振动解存在的充分必要条件。系统满足条件∫∞0ai(t)dt=∞,i=1,2。更多还原

【Abstract】 The three-dimensional differential system {u ′1=a1(t)|u2|λ1sgnu2u′2=a2(t)|u3|λ2sgnu3u′3=-a3(t)|u1|λ3sgnu1 (S)is considered under the assumptions that λi(i=1,2,3 ) are positive constants andai(t)(i=1,2,3) are positive continuous functions on [0,∞),one class of nonoscillatory solutions u of (S)(ui(t)>0 (i=1,3),u2(t)<0) having specific asymptotic growths as t→ ∞ are established. and applicate of Schauder-Tyehnoff fixed point Theorem proving in the nessary and suffcient integral conditions for the existence of eventually positive solution of(S) having specific asymptotic growths as t→ ∞.The system satisfies ∫∞0 ai(t)dt=∞,i=1,2。更多还原