ABSTRACT
Let Z = {0,±1,±2, ...} be the set of integers, and let V be a linear space of realvalued functions defined on Z. Given a function u : Z→ IR, the notation ui = u(i), i ∈ Z, is used. Fix a natural p and consider a nonlinear difference operator F : V → V given by
F[u]i ≡ φ(ui , ui+1, ..., ui+p, i), i ∈ Z, (9.1) where φ : IR p+1 × Z→ IR is a real-valued function. Therefore, (9.1) is a pth-order difference operator. Given a function g ∈ V , we study the difference equation
F[u] = g on Z, (9.2)
u ∈ V . Using techniques of linear invariant subspaces, we will describe equations (9.2), which can be reduced to finite systems of algebraic equations.
