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三阶非线性微分方程解的渐近性

On the Asymptotic Behavior of Solutions of Third-Order Nonlinear Differential Equations
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摘要 建立了三阶非线性微分方程…x+φ(x,x.,¨x)¨x+f(x,x.)=p(t,x,x.,¨x)的一切解有界和收敛到零的充分条件. Sufficient conditions under which all solutions of the third-order nonlinear differential equation x^ - +φ(x ,x ,x^- )x^- + f (x ,x^-) =p (x ,x ,x^- ) are bounded and converge to zero as t →∞.
出处 《数学的实践与认识》 CSCD 北大核心 2009年第20期188-192,共5页 Mathematics in Practice and Theory
关键词 非线性微分方程 李雅普诺夫函数 有界性 渐近性 Nonlinear differential equation Lyapunov function boundedness and asymptotic property
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参考文献5

  • 1王联 王慕秋.一类三阶非线性系统李雅普若夫函数构造之分析.应用数学学报,1983,6:309-323.
  • 2Barbashin E A. Lyapunov Functions[M]. NauKa, Moscow, 1970.
  • 3Qian C. On the global stability of third-order nonlinear differential equations[J]. Nonlinear Anal, 2000,42.. 651- 661.
  • 4Qian C. Asumptotic behavior of a third-order nonlinear differential equation[J]. J Math Anal Appl,2003,284:191- 205.
  • 5Yoshizawa T. Asymptotic behavior of solutions of a system of differential equations [J]. Contributions to Differential Equations, 1963,1 : 371-387.

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