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Lyapunov functions and convergence to steady state for differential equations of fractional order

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We study the asymptotic behaviour, as t → ∞, of bounded solutions to certain integro-differential equations in finite dimensions which include differential equations of fractional order between 0 and 2. We derive appropriate Lyapunov functions for these equations and prove that any global bounded solution converges to a steady state of a related equation, if the nonlinear potential \(\mathcal E\) occurring in the equation satisfies the Łojasiewicz inequality.

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Authors and Affiliations

  1. Departamento de Matemática y C.C., Facultad de Ciencias, University of Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

    Vicente Vergara

  2. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, 06120, Halle, Germany

    Rico Zacher

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  1. Vicente Vergara
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  2. Rico Zacher
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Vergara, V., Zacher, R. Lyapunov functions and convergence to steady state for differential equations of fractional order. Math. Z. 259, 287–309 (2008). https://doi.org/10.1007/s00209-007-0225-1

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  • DOI: https://doi.org/10.1007/s00209-007-0225-1

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