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On the asymptotics of the difference equation with a proportional delay

Kundrat P.

Opuscula Mathematica

2006

Vol. 26, no. 3

499-506

This paper deals with asymptotic properties of a vector difference equation with delayed argument Δxk = Axk +Bx(λk], 0 < λ < 1, k = 0,1,2,..., where A, B are constant matrices and the term [λk] is the integer part of λk. Our aim is to emphasize some resemblances between the asymptotic behaviour of this delay difference equation and its continuous counterpart.