Existence of different kind of solutions for discrete time equations

Denis Pennequin

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, Issue: 1, page 102-111, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Denis Pennequin. "Existence of different kind of solutions for discrete time equations." Nonautonomous Dynamical Systems 1.1 (2014): 102-111, electronic only. <http://eudml.org/doc/266633>.

@article{DenisPennequin2014,
abstract = {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.},
author = {Denis Pennequin},
journal = {Nonautonomous Dynamical Systems},
keywords = {Discrete time equation; Diagonal dominant bloc condition; periodic and almost periodic sequences; discrete time equation; diagonal dominant bloc condition},
language = {eng},
number = {1},
pages = {102-111, electronic only},
title = {Existence of different kind of solutions for discrete time equations},
url = {http://eudml.org/doc/266633},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Denis Pennequin
TI - Existence of different kind of solutions for discrete time equations
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 102
EP - 111, electronic only
AB - 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.
LA - eng
KW - Discrete time equation; Diagonal dominant bloc condition; periodic and almost periodic sequences; discrete time equation; diagonal dominant bloc condition
UR - http://eudml.org/doc/266633
ER -

References

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  1. [1] J. Andres, D. Pennequin. On Stepanov almost-periodic ocillations and their discretizations. J. Difference Eqns Appl. (2011), Zbl1257.34029
  2. [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.[Crossref] Zbl1278.34065
  3. [3] J. Blot, B. Crettez. On the smoothness of optimal paths. Decisions in Economics and Finance.27(2004), 1-34, DOI: 10.1007/s10203-004-0042-5[Crossref] Zbl1091.91053
  4. [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-x[Crossref] Zbl1141.91035
  5. [5] J. Blot, D. Pennequin. Existence and structure results on almost periodic solutions of difference equations.J. Differ. Equa. Appl.7 (2001), 383-402. Zbl1005.39011
  6. [6] P. G. Ciarlet, Introduction à l'analyse numérique matricielle età l'optimisation, Masson, Paris, 1994 Zbl0488.65001
  7. [7] C. Corduneanu, Almost Periodic Functions, Chelsea Publ. Comp., 1989. 
  8. [8] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009. Zbl1163.34002
  9. [9] D.G. De Figueiredo, Lectures on the Ekeland variational principle with applications and detours, Tata Institute of fundamental Research, Bombay, 1989 
  10. [10] C. Kahane. Stability of Solutions of Linear Systems with Dominant Main Diagonal. Proc. Amer. Math. Soc.33 (1972), No. 1 69-71.[Crossref] Zbl0241.34056
  11. [11] J.-L. Mauclaire, Intégration et Théorie des Nombres, Hermann, Paris, 1986. 
  12. [12] D. Pennequin. Notion of WeakVariational Solutions for Almost Periodic or More General Problems. African Diaspora J. Math.15 (2013) no 2,101-110. Zbl1298.34108

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