# Existence of different kind of solutions for discrete time equations

Nonautonomous Dynamical Systems (2014)

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

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topDenis 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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- [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] 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] 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] 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] P. G. Ciarlet, Introduction à l'analyse numérique matricielle età l'optimisation, Masson, Paris, 1994 Zbl0488.65001
- [7] C. Corduneanu, Almost Periodic Functions, Chelsea Publ. Comp., 1989.
- [8] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009. Zbl1163.34002
- [9] D.G. De Figueiredo, Lectures on the Ekeland variational principle with applications and detours, Tata Institute of fundamental Research, Bombay, 1989
- [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] J.-L. Mauclaire, Intégration et Théorie des Nombres, Hermann, Paris, 1986.
- [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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