UNIFORM ANTI-MAXIMUM PRINCIPLE FOR A CLASS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS OF SECOND ORDER DIFFERENCE EQUATIONS

Rui Wang; Yanqiong Lu; Ruyun Ma

doi:10.11948/20260029

2026 Volume 16 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(6): 2875-2886

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Rui Wang, Yanqiong Lu, Ruyun Ma. UNIFORM ANTI-MAXIMUM PRINCIPLE FOR A CLASS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS OF SECOND ORDER DIFFERENCE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2875-2886. doi: 10.11948/20260029

Citation:

Rui Wang, Yanqiong Lu, Ruyun Ma. UNIFORM ANTI-MAXIMUM PRINCIPLE FOR A CLASS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS OF SECOND ORDER DIFFERENCE EQUATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(6): 2875-2886. doi: 10.11948/20260029

UNIFORM ANTI-MAXIMUM PRINCIPLE FOR A CLASS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS OF SECOND ORDER DIFFERENCE EQUATIONS

1.
School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi 710071, China
2.
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China

Author Bio: Email: wr393023294@163.com(R. Wang); Email: luyq8610@126.com(Y. Lu)
Corresponding author: Email: ryma@xidian.edu.cn(R. Ma)
Fund Project: The authors were supported by National Natural Science Foundation of China (12461036, 12361040)

Abstract

Abstract

where $ a, b\in[0, \infty), \; D $ denotes the forward difference operator defined by $ D u(t) = u(t+1)-u(t) $, $ T\geq 3 $ is a fixed positive integer, $ [1, T]_{\mathbb{Z}}:=\{1, 2, \cdot\cdot\cdot, T\}, \; f:[1, T]_{\mathbb{Z}}\to[0, \infty) $, and $ \lambda\in\mathbb{R} $ is a parameter. We establish a uniform anti-maximum principle for such problem. As an application of the main result, we obtain the existence of solutions to a class of nonlinear problems via the method of lower and upper solutions and fixed point theorem.
- Second-order operator /
- difference equations /
- uniform anti-maximum principle /
- principal eigenvalue
MSC: 39A05, 39A12, 39A60, 39A70

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References

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