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Two-point boundary value problems for first order causal difference equations. (English) Zbl 1464.39012

Summary: This paper focuses on two-point boundary value problem for first order causal difference equations. We will start with two new comparison theorems. Then, by utilizing these theorems and fixed point theorems, we obtain the existence of solutions for the corresponding linear problem. By applying monotone iterative technique, sufficient conditions for the existence of extremal solutions are also established. The results of this paper extend some existing results in the literature. Finally, two examples to show the usefulness of our results are exhibited.

MSC:

39A27 Boundary value problems for difference equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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