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Stability of nonlinear time-varying perturbed differential equations

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Abstract

The goal of this paper is twofold. The first part presents a converse Lyapunov theorem for the notion of uniform practical exponential stability of nonlinear differential equations in presence of small perturbation. This class of nonlinear differential equations can be viewed as parametric differential equations. The second part provides the classical perturbation method of seeking an approximate solution as a finite Taylor expansion of the exact solution. The practical asymptotic validity on the approximate is established on infinite-time interval. Finally, we give a numerical example to prove the validity of our methods.

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Authors and Affiliations

  1. Department of Mathematics, Higher Institute of Electronics and Communication of Sfax, Street Menzel Chaker km 0.5, B.P. 261, 3038, Sfax, Tunisia

    Bassem Ben Hamed

  2. Department of Mathematics, Higher Institute of Applied Science and Technology of Gabès, Street Amor Ben El Khatab, 6029, Gabès, Tunisia

    Zaineb Haj Salem

  3. Department of Mathematics, Faculty of Science of Sfax, BP 1171, Street Soukra, 3000, Sfax, Tunisia

    Mohamed Ali Hammami

Authors
  1. Bassem Ben Hamed
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  2. Zaineb Haj Salem
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  3. Mohamed Ali Hammami
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Correspondence to Bassem Ben Hamed.

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Ben Hamed, B., Haj Salem, Z. & Hammami, M.A. Stability of nonlinear time-varying perturbed differential equations. Nonlinear Dyn 73, 1353–1365 (2013). https://doi.org/10.1007/s11071-013-0868-x

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  • DOI: https://doi.org/10.1007/s11071-013-0868-x

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