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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

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.

Keywords

ordinary differential equations;Lyapunov′s stability;ultimate boundedness;nonlinear transformations

References

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

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