ON SOLVABILITY OF ONE DIFFERENCE EQUATION

Abstract

We consider a system of difference equation similar to those that appear as description of cumulative sums. Using Hamel bases, we construct pathological solutions to this system for constant right-hand sides. Also we show that bounded so- lutions 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