Existence of almost periodic solutions of discrete time equations

Pages: 51 - 60, Volume 7, Issue 1, January 2001

doi:10.3934/dcds.2001.7.51       Abstract        Full Text (164.4K)       Related Articles

Denis Pennequin - CERMSEM, M.S.E., Université de Paris 1, 106-112 bd de l'Hôpital, 75647 PARIS Cedex 13, France (email)

Abstract: In this paper, we study almost periodic (a.p.) solutions of discrete dynamical systems. We first adapt some results on a.p. differential equations to a.p. difference equations, on the link between boundedness of solutions and existence of a.p. solutions. After, we obtain an existence result in the space of the Harmonic Synthesis for an equation $A_t (x_t,...,x_{t+p})=0$ when the dependance of $A$ on $t$ is a.p. and when $A_t$ and $D A_t$ are uniformly Lipschitz and satisfy another condition which is exactly the extension of a simple one for the basic linear system. The main tools for that are Nonlinear Functional Analysis and the Newton method.

Keywords:  Discrete Time Equations, almost periodic solutions, bounded solutions, Newton’s method.
Mathematics Subject Classification:  39A10, 43A60, 93C55.

Received: June 2000;      Published: November 2000.