In this research, we consider a nonhomogeneous linear difference equation with constant coefficients of order k greater than or equal to 2 subject to boundary conditions that split into two groups: initial and final conditions. We establish necessary and / or sufficient conditions on the distribution(s) of the zeros of the associated characteristic polynomial that ensure the existence of a unique solution.
"Discrete Boundary Value Problems with Initial and Final Conditions." Methods Appl. Anal. 11 (1) 033 - 040, March 2004.