In this paper, by means of the appropriate Green’s function, an integral representation for the solutions of certain boundary value problems for second-order difference equations on (quadratic and q-quadratic) non-uniform lattices is presented. As a consequence, using fixed point theory, new results for the existence and uniqueness of the solution are proved on non-uniform lattices. ; MSC: 34B27, 39A20, 34A05, 34B05.