Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations

In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter λ. Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for this problem and obtain some determined open intervals of the parameter λ for the existence of at least two positive solutions. In the end, we give two examples to illustrate our main results.