| 一类三维微分系统正值解的结构(英文) |
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| 引用本文： | 杨云芳.一类三维微分系统正值解的结构(英文)[J].大学数学,2012(4):39-45. |
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| 作者姓名： | 杨云芳 |
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| 作者单位： | 牡丹江医学院数学教研室 |
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| 基金项目： | the Education Science and Technology Research of Heilongjiang Provincial Department(11533077) |
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| 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.
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| 关 键 词： | 正值解 极端解 三维微分系统 |
The Structure of the Set of Nonoscillatory Solutions of Three-Dimensional Differential Systems |
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| YANG Yun-fang.The Structure of the Set of Nonoscillatory Solutions of Three-Dimensional Differential Systems[J].College Mathematics,2012(4):39-45. |
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| Authors: | YANG Yun-fang |
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| Institution: | YANG Yun-fang(Department of Mathematics,Mudanjiang Medical University,Mudanjiang,Heilongjiang 157011,China) |
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| Abstract: | 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 u1. 1(S) is considered under the assumptions thatλ i(i=1,2,3) are positive constants and a i(t)(i=1,2,3) are positive continuous functions on 0,∞),and several classes of nonoscillatory solutions uof(S) having specific asymptotic growths as t→ ∞are established.The system satisfies ∫0∞ ai(t)dt=∞,i=1,2,3. |
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| Keywords: | positive solution extreme solution the three-dimensional differential system |
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