Note on bounded solutions to nonhomogenous linear difference equations

Stevic, Stevo
Iricanin, Bratislav
Smarda, Zdenek
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Texas State University, Department of Mathematics
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.
Nonhomogeneous linear difference equation, Bounded solution, Contraction mapping principle, Integer domain
Stevic, S., Iricanin, B., & Smarda, Z. (2017). Note on bounded solutions to nonhomogenous linear difference equations. <i>Electronic Journal of Differential Equations, 2017</i>(286), pp. 1-22.