A boundary value problem of a generalised linear discrete time system with no solutions and infinitely many solutions

Abstract: In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into consideration the case that the coefficients are square constant matrices with the leading coefficient singular and provide optimal solutions. Numerical examples are given to justify our theory.