Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE STABILITY AND INSTABILITY OF A CLASS OF NONLINEAR NONAUTONOMOUS ORDINARY DIFFERENTIAI, EQUATIONS

  • Sen, M.DeLa (Instituto de Investigaciony Desarrollo de Procesos IIDP, Facultad de Ciencias. Universidad del Pa′is Vasco Leioa(Bizkaia))
  • Published : 2003.05.01
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Abstract

This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.

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References

  1. Nonlinear ordinary differential equations and their applications P.L.Sachdev
  2. Nonlinear systems analysis M.Vidyasagar

Cited by

  1. Lie symmetries, Lagrangians and Hamiltonian framework of a class of nonlinear nonautonomous equations vol.75, 2015, https://doi.org/10.1016/j.chaos.2015.02.021