EIGENVALUE PROBLEM FOR FRACTIONAL DIFFERENCE EQUATION WITH NONLOCAL CONDITIONS

Yongshun Zhao; Shurong Sun

doi:10.11948/20180305

2021 Volume 11 Issue 1

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Yongshun Zhao, Shurong Sun. EIGENVALUE PROBLEM FOR FRACTIONAL DIFFERENCE EQUATION WITH NONLOCAL CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 32-44. doi: 10.11948/20180305

Citation:

Yongshun Zhao, Shurong Sun. EIGENVALUE PROBLEM FOR FRACTIONAL DIFFERENCE EQUATION WITH NONLOCAL CONDITIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 32-44. doi: 10.11948/20180305

EIGENVALUE PROBLEM FOR FRACTIONAL DIFFERENCE EQUATION WITH NONLOCAL CONDITIONS

Yongshun Zhao¹,
Shurong Sun^1, ,

1.
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Corresponding author: Email address:sshrong@163.com(S. Sun)
Fund Project: This research is supported by the Natural Science Foundation of China(62073153, 61803176), also supported by Shandong Provincial Natural Science Foundation (ZR2020MA016)

Abstract

Abstract

In this work, we investigate a class of boundary value problem for fractional difference equation with nonlocal conditions
$ \begin{cases}\Delta^{\nu}u(t)+\lambda f(t+\nu-1, u(t+\nu-1)) = 0, t\in\mathbb{N}_{0}^{b+1},\\ u(\nu-2) = h(u), \Delta u(\nu+b) = g(u), \end{cases} $

where $ 1<\nu\leq2 $ is a real number, $ f:\mathbb{N}_{\nu-1}^{\nu+b}\times\mathbb{R}\rightarrow(0, +\infty) $ is a continuous function, $ g, h $ are given functionals, $ b\geq2 $ is an integer, $ \lambda>0 $ is a parameter. By upper and lower solutions method, we can present the existence result of positive solutions. The eigenvalue intervals to this problem are studied by the properties of the Green function and Guo-Krasnosel'skii fixed point theorem in cones.
- Boundary value problem /
- fractional difference equation /
- positive solutions /
- eigenvalue problem /
- fixed-point theorem
MSC: 65Q10, 45M20, 47A75

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