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.
@article{bwmeta1.element.doi-10_2478_msds-2014-0005,
author = {Denis Pennequin},
title = {Existence of different kind of solutions for discrete time equations},
journal = {Nonautonomous Dynamical Systems},
volume = {1},
year = {2014},
zbl = {1304.93048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_msds-2014-0005}
}
Denis Pennequin. Existence of different kind of solutions for discrete time equations. Nonautonomous Dynamical Systems, Tome 1 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_msds-2014-0005/
[1] J. Andres, D. Pennequin. On Stepanov almost-periodic ocillations and their discretizations. J. Difference Eqns Appl. (2011), | Zbl 1257.34029
[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] | Zbl 1278.34065
[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] | Zbl 1091.91053
[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] | Zbl 1141.91035
[5] J. Blot, D. Pennequin. Existence and structure results on almost periodic solutions of difference equations.J. Differ. Equa. Appl.7 (2001), 383-402. | Zbl 1005.39011
[6] P. G. Ciarlet, Introduction à l'analyse numérique matricielle età l'optimisation, Masson, Paris, 1994 | Zbl 0488.65001
[7] C. Corduneanu, Almost Periodic Functions, Chelsea Publ. Comp., 1989.
[8] C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009. | Zbl 1163.34002
[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] | Zbl 0241.34056
[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. | Zbl 1298.34108