Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

Mathematical Citation Quotient (MCQ) 2018: 0.62

Open Access
See all formats and pricing
More options …

Existence of different kind of solutions for discrete time equations

Denis Pennequin
  • Corresponding author
  • Université Paris 1 Panthéon-Sorbonne, Laboratoire SAMM, Centre PMF, 90 rue de Tolbiac, 75634 PARIS Cedex 13, France
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-08-15 | DOI: https://doi.org/10.2478/msds-2014-0005


The aim of this paper is to extend the classical linear condition concerning diagonal dominant bloc matrix to fully nonlinear equations. Even if assumptions are strong, we obtain an explicit condition which exactly extend the one known in linear case, and the setting allows also to consider bicontinuous operator instead of the schift and as particular case, we receive periodic or almost periodic solutions for discrete time equations.

Keywords: Discrete time equation; Diagonal dominant bloc condition; periodic and almost periodic sequences


  • [1] J. Andres, D. Pennequin. On Stepanov almost-periodic ocillations and their discretizations. J. Difference Eqns Appl. (2011),Google Scholar

  • [2] J. Andres, D. Pennequin. On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations. Proc. Amer. Math. Soc. 140 (2012), 2825-2834.CrossrefGoogle Scholar

  • [3] J. Blot, B. Crettez. On the smoothness of optimal paths. Decisions in Economics and Finance. 27(2004), 1-34, DOI: 10.1007/s10203-004-0042-5CrossrefGoogle Scholar

  • [4] J. Blot, B. Crettez. On the smoothness of optimal paths II: some turnpike results. Decisions in Economics and Finance. 30 (2004), 137-150, 2004, DOI: 10.1007/s10203-007-0072-xCrossrefGoogle Scholar

  • [5] J. Blot, D. Pennequin. Existence and structure results on almost periodic solutions of difference equations.J. Differ. Equa. Appl. 7 (2001), 383-402.Google Scholar

  • [6] P. G. Ciarlet, Introduction à l'analyse numérique matricielle età l'optimisation, Masson, Paris, 1994Google Scholar

  • [7] C. Corduneanu, Almost Periodic Functions, Chelsea Publ. Comp., 1989.Google Scholar

  • [8] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009.Google Scholar

  • [9] D.G. De Figueiredo, Lectures on the Ekeland variational principle with applications and detours, Tata Institute of fundamental Research, Bombay, 1989Google Scholar

  • [10] C. Kahane. Stability of Solutions of Linear Systems with Dominant Main Diagonal. Proc. Amer. Math. Soc. 33 (1972), No. 1 69-71.CrossrefGoogle Scholar

  • [11] J.-L. Mauclaire, Intégration et Théorie des Nombres, Hermann, Paris, 1986.Google Scholar

  • [12] D. Pennequin. Notion of WeakVariational Solutions for Almost Periodic or More General Problems. African Diaspora J. Math. 15 (2013) no 2,101-110.Google Scholar

About the article

Received: 2013-12-29

Accepted: 2014-05-11

Published Online: 2014-08-15

Citation Information: Nonautonomous Dynamical Systems, Volume 1, Issue 1, ISSN (Online) 2299-3193, DOI: https://doi.org/10.2478/msds-2014-0005.

Export Citation

© 2014 Denis Pennequin. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in