Discrete third-order three-point right-focal boundary value problems
We are concerned with the discrete right-focal boundary value problem Delta(3)x(t) = f(t, x(t + 1)), x(t(1)) = Deltax(t(2)) = Delta(2)x(t(3)) = 0, and the eigenvalue problem Delta(3)x(t) = lambdaa(t) f (x(t + 1)) with the same boundary conditions, where t(1) < t(2) < t(3). Under various assumptions on f, a, and a, we prove the existence of positive solutions of both problems by applying a fixed-point theorem. (C) 2003 Elsevier Science Ltd. All rights reserved.
eigenvalues difference equations green's function fixed points cone multiple solutions