Two-Point Boundary Value Problems for First Order Causal Difference Equations

Wen-Li Wang, Jing-Feng Tian () and Wing-Sum Cheung
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Wen-Li Wang: China University of Geosciences, Great Wall College
Jing-Feng Tian: North China Electric Power University
Wing-Sum Cheung: University of Hong Kong

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1399-1416

Abstract: Abstract 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.

Keywords: Two-point boundary value problem; causal difference equations; monotone iterative technique; extremal solutions; 34B15; 39A10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0473-x

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