Existence of different kind of solutions for discrete time equations

• Autorzy: Denis Pennequin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2014
• Tom: 1
• Numer: 1

Daty

otrzymano

2013-12-29

zaakceptowano

2014-05-11

online

2014-08-15

Twórcy

autor

Denis Pennequin

• Université Paris 1 Panthéon-Sorbonne, Laboratoire SAMM, Centre PMF, 90 rue de Tolbiac, 75634 PARIS Cedex 13, France

Bibliografia

• [1] J. Andres, D. Pennequin. On Stepanov almost-periodic ocillations and their discretizations. J. Difference Eqns Appl. (2011),
• [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]
• [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]
• [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]
• [5] J. Blot, D. Pennequin. Existence and structure results on almost periodic solutions of difference equations.J. Differ. Equa. Appl.7 (2001), 383-402.
• [6] P. G. Ciarlet, Introduction à l'analyse numérique matricielle età l'optimisation, Masson, Paris, 1994
• [7] C. Corduneanu, Almost Periodic Functions, Chelsea Publ. Comp., 1989.
• [8] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009.
• [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]
• [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.

Identyfikatory

DOI

10.2478/msds-2014-0005