Nonlocal boundary value problems for discrete systems

Our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete, nonlinear systems subject to multipoint boundary conditions. The criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear, homogeneous boundary value problems. Our analysis is based on the Lyapunov–Schmidt Procedure and Brouwerʼs Fixed Point Theorem. The results presented extend the previous work of D. Etheridge and J. Rodríguez (1996, 1998) [5,6] and J. Rodríguez and P. Taylor (2007) [18,19].