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On the Solvability of Nonlinear Discrete Boundary Value Problems

In this paper, we establish sufficient conditions for the existence of solutions to nonlinear, second-order, discrete boundary value problems of the form: subject to and The nonlinearity is assumed to be continuous, but not necessarily differentiable. We provide conditions for the solvability of the boundary value problem when f is of the “perturbation type” as well as when f is of “slow growth”.