Abstract
In this paper, we study some properties of q-Lidstone polynomials by using Green's function of certain q-differential systems. The q-Fourier series expansions of these polynomials are given. As an application, we prove the existence of solutions for the linear q-difference equations
(-1)(n)D(q-1)(2n)y(x) = phi(x,y(x), D-q-1 y(x), D(q-1)(2)y(x), ... , D(q-1)(k)y(x)),
subject to the boundary conditions
D(q-1)(2j)y(0) = (beta)j, D(q-1)(2j)y(1) = gamma(j) (beta(j), gamma(j) is an element of C, j = 0,1,..., n - 1),
where n is an element of N and 0 <= k <= 2n - 1. These results are a q-analogue of work by Agarwal and Wong of 1989.