一类带有p-Laplacian算子的分数阶积分边值问题的多重正解
Multiple Positive Solutions for Fractional In-tegral Boundary Value Problems with p-Laplacian Operators
摘要: 本文研究了一类带有p-Laplacian算子的分数阶积分边值问题正解的存在性，通过研究格林函数的性质，运用锥拉伸锥压缩不动点定理以及Leggett-Williams不动点定理，获得了该边值问题至少存在一个正解及三个正解的充分条件，并给出实例验证所得结论。
Abstract: Studying the properties of Green’s function and using the cone stretching cone compression fixed point theorem and the Leggett-Williams fixed point theorem, this paper studies the existence of positive solutions for a class of fractional integral boundary value problems with p-Laplacian oper-ators, obtains sufficient conditions for the existence of at least one positive solution and three posi-tive solutions to the boundary value problems, and gives some examples illustrating the results obtained.
文章引用：武瑜, 刘畅. 一类带有p-Laplacian算子的分数阶积分边值问题的多重正解[J]. 应用数学进展, 2023, 12(3): 1340-1350. https://doi.org/10.12677/AAM.2023.123136

参考文献

[1] 白占兵. 分数阶微分方程边值问题理论及其应用[M]. 北京: 中国科学技术出版社, 2013.
[2] Mena, J.C., Sauco, J.H. and Kishin, S. (2021) Existence and Uniqueness of Positive Solutions for a Class of Singular Fractional Differential Equation with Infinite-Point Boundary Value Conditions. The Royal Academy of Sciences, 115, 1-12. [Google Scholar] [CrossRef] 
[3] 郭大均. 非线性泛函分析[M]. 第三版. 北京: 中国科学技术出版社, 2013.
[4] Zhang. X.Q. (2015) Positive Solutions for a Class of Singular Fractional Differential Equation with Infinite-Point Boundary Value Conditions. Applied Mathematics Letters, 39, 22-27. [Google Scholar] [CrossRef] 
[5] Zhai, C.B. and Wang, L. (2017) Some Existence, Uniqueness Re-sults on Positive Solutions for a Fractional Differential Equation with Infinite-Point Boundary Conditions. Nonlinear Analysis: Modelling and Control, 22, 566-577. [Google Scholar] [CrossRef] 
[6] Wang, Y., Liu, L.S. and Wu, Y.H. (2015) Extremal Solutions for p-Laplacian Fractional Integro-Differential Equation with Integral Conditions on Infinite Intervals via Iterative Computa-tion. Advances in Difference Equations, 24, 1-14. [Google Scholar] [CrossRef] 
[7] Wang, W.X., Duan, J.Y. and Guo, X.Z. (2022) Successive Itera-tion and Positive Solutions for Fractional Integral Boundary Value Problem with p-Laplacian Operator. Mathematica Ap-plicata, 35, 147-155.
[8] Tian, Y.S., Bai, Z.B. and Sun, S.J. (2019) Positive Solutions for a Boundary Value Problem of Fractional Differential Equation with p-Laplacian Operator. Advances in Difference Equations, 2019, 1-14. [Google Scholar] [CrossRef] 
[9] 田元生, 李小平, 葛渭高. p-Laplacian分数阶微分方程边值问题正解的存在性[J]. 应用数学学报, 2018, 41(4): 529-539.
[10] He, Y. (2018) Extremal Solutions for p-Laplacian Fractional Differential Systems Involving the Riemann-Liouville Integral Boundary Conditions. Advances in Difference Equations, 2018, 1-11. [Google Scholar] [CrossRef] 

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