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Lyapunov, A.M. (1902) On the Series, Encountered in the Theory of Linear Second Order Differential Equations with Periodic Coefficients. Academy of Science Notes on the Physics-Mathematical Department, VIII, 1-70. (In Russian)

has been cited by the following article:

• TITLE: Comparison on Sufficient Conditions for the Stability of Hill Equation: An Arnold’s Tongues Approach

  AUTHORS: Carlos A. Franco, Joaquin Collado

  KEYWORDS: Periodic Differential Equations, Stability Sufficient Criteria, Hill Equation, Hamiltonian, Lyapunov Characteristic Constant

  JOURNAL NAME: Applied Mathematics, Vol.8 No.10, October 31, 2017

  ABSTRACT: It is known that the solutions of a second order linear differential equation with periodic coefficients are almost always analytically impossible to obtain and in order to study its properties we often require a computational approach. In this paper we compare graphically, using the Arnold Tongues, some sufficient criteria for the stability of periodic differential equations. We also present a brief explanation on how the authors, of each criterion, obtained them. And a comparison between four sufficient stability criteria and the stability zones found by perturbation methods is presented.