Electron. J. Differential Equations, Vol. 2017 (2017), No. 286, pp. 1-22.

Note on bounded solutions to nonhomogenous linear difference equations

Stevo Stevic, Bratislav Iricanin, Zdenek Smarda

By using a solvability method along with the contraction mapping principle quite recently has been presented an interesting method for showing the existence of a unique bounded solution to a nonhomogenous linear second-order difference equation on the set of nonnegative integers. It is a natural question if the combination of the method and principle can be applied in showing the existence of bounded solutions to some higher-order generalizations of the equation. Here, among others, we give a positive answer to the question for the case of a nonhomogenous linear difference equation of third order. Moreover, the equation is studied on the whole integer domain Z.

Submitted July 25, 2017. Published November 14, 2017.
Math Subject Classifications: 39A06, 47H09, 39A45.
Key Words: Nonhomogeneous linear difference equation; bounded solution; contraction mapping principle; integer domain.

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Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III, 11000 Beograd, Serbia
email: sstevic@ptt.rs
Bratislav Iricanin
Faculty of Electrical Engineering
Belgrade University
Bulevar Kralja Aleksandra 73
11000 Beograd, Serbia
email: iricanin@etf.rs
Zdenek Smarda
Brno University of Technology
Faculty of Electrical Engineering and Communication
Department of Mathematics
Technicka 3058/10, CZ
616 00 Brno, Czech Republic
email: smarda@feec.vutbr.cz

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