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Reduction principle in the theory of stability of difference equations

Pages: 864 - 874, Issue Special, September 2007

 Abstract        Full Text (172.7K)              

Andrejs Reinfelds - Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvăris 29, Rīga, LV-1459, Latvia (email)
Klara Janglajew - Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland (email)

Abstract: The reduction principle is generalized to the case of the nonautonomous difference equations in Banach space whose right-handed side is allowed to be noninvertible and whose linear part satisfies weaker condition than exponential dichotomy.

Keywords:  Reduction principle, invariant manifold, stability of solutions, asymptotic phase.
Mathematics Subject Classification:  Primary: 39A11, 37B55; Secondary: 37B25, 39A12.

Received: September 2006;      Revised: February 2007;      Published: September 2007.