On solvability of one difference equation

I. A. Chernov<sup>ab

a</sup> Petrozavodsk State University, 33, Lenina pr., Petrozavodsk 185910, Russia
^b Inst. Appl. Math. Research of Karelian Research Centre of Russian Academy of Sciences, 11, Pushkinskaya st., Petrozavodsk 185910, Russia

Abstract: We consider a system of difference equation similar to those that appear as a description of cumulative sums. Using Hamel bases, we construct pathological solutions to this system for constant right-hand sides. Also we show that bounded solutions do not exist for non-zero right-hand sides, while only constants can be solutions in the homogeneous case.

Keywords: difference equations, Hamel basis, pathological solutions, existence and uniqueness.

UDC: 517.929.2

MSC: 39A06

Received: 30.12.2016
Revised: 13.03.2017
Accepted: 05.04.2017

Language: English

DOI: 10.15393/j3.art.2017.3550

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