Comparable solutions to n(th)-order linear difference equations

We consider the nth-order linear difference equation l(n)y(t) = L(n)y(t) + q(t)y (t + [n/2]) = 0, for t is an element of [a,b] where q(t) is a real-valued function defined o n [a, b]. We define the (formal) adjoint operator l(n)* of l(n) by l(n)*z(t) = L-n*z(t) + (-1)(n)q(t)z (t + [n/2]), for t is an element of [a, b]. We compare boundary value solutions of l(n)y (t) = 0 to similar solutions of the adjoint equation l(n)*z(t) = 0. (C) 200 0 Elsevier Science Ltd. All rights reserved.