| 关子齐次微分方程的积分曲线 |
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| 引用本文： | 李梧生. 关子齐次微分方程的积分曲线[J]. 汕头大学学报(自然科学版), 1989, 0(1) |
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| 作者姓名： | 李梧生 |
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| 作者单位： | 汕头大学数学系 |
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| 摘 要： | 记所论微分方程为(E_λ)_n,本文拓广的不变直线法,在(E_λ)_n的“有理相曲线”与临界、中介水平线”的交、切点与型号间建立起对应关系.依次以各水平线上交、切点型号串得的型列为行,使构成(E_λ)_n的型阵.它表达出λ遍取不同实数值(由-∞至,+∞)时,(E_λ)_n积分曲线的定性变化图景.实际上,它就是的均匀旋转向量场的完全族.
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| 关 键 词： | 积分曲线 微分方程定性论 |
Integral Curves of the Homogeneous Differential Equation |
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| Li Wusheng. Integral Curves of the Homogeneous Differential Equation[J]. Journal of Shantou University(Natural Science Edition), 1989, 0(1) |
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| Authors: | Li Wusheng |
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| Affiliation: | Department of Mathematics |
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| Abstract: | The differential equation under discussion is denoted by f(E_λ)_n. (λ varies from-∝ to +∝). In this paper, we establish a corresponding relation between the "actual type-matrix" of (E_λ)_n and the graph fromed by "rational phase curve" "critical horizontal line" and "intermediary horizontal line". The qualitative picture corresponding to the "actual type-matrix", in fact, is total family of the uniformly rotated vector fieldof |
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| Keywords: | Intgral curves Qualitative theory of ordinary differential equations |
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