| 一类二阶非线性微分方程解的渐近性态 |
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| 引用本文： | 程玉民 沈祖炎. 一类二阶非线性微分方程解的渐近性态[J]. 同济大学学报(自然科学版), 1996, 24(5): 568-573 |
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| 作者姓名： | 程玉民 沈祖炎 |
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| 作者单位： | 同济大学建筑工程系 |
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| 摘 要： | 在一定条件下，研究了一类二阶非线性微分方程的解的渐近性态，并研究了其解的单调性和可延拓性条件以及其解有界的充分必要条件，得到了这类介非线性微分方程的解与二阶线性微分方程的解的渐近关系，以及这两个方程的某些解的等价性条件。
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| 关 键 词： | 非线性微分方程 单调性 有界性 渐近性态 |
On the Asymptotic Behavior of the Solutions of a Class of Second-order Nonlinear Differential Equations |
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| Cheng Yumin,Shen Zuyan. On the Asymptotic Behavior of the Solutions of a Class of Second-order Nonlinear Differential Equations[J]. Journal of Tongji University(Natural Science), 1996, 24(5): 568-573 |
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| Authors: | Cheng Yumin Shen Zuyan |
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| Abstract: | In this paper, we investigate the asympototic behavior of solutions of a class of second order nonlinear differential equation. We discuss the conditions of monotonicity and continuation, and the sufficient and necessary conditions of boundness of the solutions of the equation. And we obtain the asymptotic relationship between the solutions of the equation and those of a class of second order linear differential equation and the equivalent condition of some solutions of the equations. |
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| Keywords: | Nonlinear differential equation Monotonicity Boundness Continuation Asymptotic behavior |
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