POSITIVE SOLUTIONS FOR A NONLINEAR DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM WITH A $ P $-LAPLACIAN OPERATOR

Wei Cheng; Jiafa Xu; Donal O'Regan; Yujun Cui

doi:10.11948/20190051

2019 Volume 9 Issue 5

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Wei Cheng, Jiafa Xu, Donal O'Regan, Yujun Cui. POSITIVE SOLUTIONS FOR A NONLINEAR DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM WITH A $ P $-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1959-1972. doi: 10.11948/20190051

Citation:

Wei Cheng, Jiafa Xu, Donal O'Regan, Yujun Cui. POSITIVE SOLUTIONS FOR A NONLINEAR DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM WITH A $ P $-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1959-1972. doi: 10.11948/20190051

POSITIVE SOLUTIONS FOR A NONLINEAR DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM WITH A $ P $-LAPLACIAN OPERATOR

1.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
2.
Key Laboratory for Optimization and Control of the Ministry of Education, Chongqing Normal University, Chongqing 400047, China
3.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
4.
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

Corresponding author: Email address: cyj720201@163.com(Y. Cui)
Fund Project: The authors were supported by Natural Science Foundation of China (Nos. 11571207, 11601048, 51774197), Natural Science Foundation of Chongqing (No. cstc2016jcyjA0181), the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJQN201800533), Natural Science Foundation of Chongqing Normal University (No. 16XYY24), and the Tai'shan Scholar Engineering Construction Fund of Shandong Province of China

Abstract

Abstract

In this paper using the monotone iterative technique we establish the existence and uniqueness of positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator. Also we discuss an iterative sequence which yields the approximate solution for this problem.
- Fractional difference equations /
- $p$-Laplacian /
- positive solutions /
- Iteration
MSC: 34B10, 34B18, 34A34, 45G15, 45M20

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References

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