一类含有参数的分数阶微分方程边值问题的单调算子方法
Monotone Operator Method for a Class of Boundary Value Problem of Fractional Differential Equations with Parameter
DOI: 10.12677/PM.2021.111002, PDF,  被引量    国家自然科学基金支持
作者: 邵宏宇, 王文霞*：太原师范学院数学系，山西 晋中
关键词: 分数阶微分方程；边值问题；正解；Fractional Differential Equation； Boundary Value Problem； Positive Solution
摘要: 利用单调算子和混合单调算子以及格林函数的性质，研究了一类含有参数的分数阶微分方程边值问题正解的存在唯一性，得到了存在唯一正解的充分条件和正解的若干性质，最后给出了两个具体的例子。
Abstract: By using monotone operator, mixed monotone operator and properties of Green function, the ex-istence and uniqueness of monotone operator method for a class of boundary value problem of fractional differential equations with parameter are studied and some sufficient conditions for the existence and uniqueness of a positive solution are obtained. Finally, two examples are given to illustrate the main results.
文章引用：邵宏宇, 王文霞. 一类含有参数的分数阶微分方程边值问题的单调算子方法[J]. 理论数学, 2021, 11(1): 7-15. https://doi.org/10.12677/PM.2021.111002

参考文献

[1] Bai, Z.B. (2012) Eigenvalue Intervals for a Class of Fractional Boundary Value Problem. Computers & Mathematics with Ap-plications, 64, 3253-3257. [Google Scholar] [CrossRef] 
[2] Jiang, W.H. (2013) Eigenvalue Interval for Multi-Point Boundary Value Problems of Fractional Differential Equations. Applied Mathematics and Computation, 219, 4570-4575. [Google Scholar] [CrossRef] 
[3] Sun, S.R., Zhao, Y.G., Han, Z.L. and Liu, J. (2013) Eigen-value Problem for a Class of Nonlinear Fractional Differential Equations. Annals of Functional Analysis, 4, 25-39. [Google Scholar] [CrossRef] 
[4] Zhai, C.B. and Xu, L. (2014) Properties of Positive Solutions to a Class of Four-Point Boundary Value Problem of Caputo Fractional Differential Equations with a Parameter. Communications in Non-linear Science and Numerical Simulation, 19, 2820-2827. [Google Scholar] [CrossRef] 
[5] Zhang, X.G., Liu, L.S., et al. (2014) The Eigenvalue for a Class of Singular p-Laplacian Fractional Differential Equations Involving the Riemann-Stieltjes Integral Boundary Condition. Applied Mathematics and Computation, 235, 412-422. [Google Scholar] [CrossRef] 
[6] Wang, G.T., Liu, S.Y. and Zhang, L.H. (2014) Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions. Abstract and Applied Analysis, 2014, Article ID: 916260. [Google Scholar] [CrossRef] 
[7] Wang, W.X. and Guo, X.T. (2016) Eigenvalue Problem for Fractional Dif-ferential Equations with Nonlinear Integral and Disturbance Parameter in Boundary Conditions. Boundary Value Problems, 2016, Article No. 42. [Google Scholar] [CrossRef] 
[8] Su, X.F., Jia, M. and Li, M.M. (2016) The Existence and Nonexistence of Positive Solutions for Fractional Differential Equations with Nonhomogeneous Boundary Conditions. Advances in Difference Equations, 2016, Article No. 30. [Google Scholar] [CrossRef] 
[9] 郭大均. 非线性泛函分析(第三版) [M]. 北京: 高等教育出版社, 2015.
[10] Zhai, C.B. and Wang, F. (2015) Properties of Positive Solutions for the Operator Equation Ax = λx and Applications to Fractional Differential Equations with Integal Boundary Conditions. Advances in Difference Equations, 2015, Article No. 366. [Google Scholar] [CrossRef] 
[11] Zhai, C.B. and Zhang, L.L. (2011) New Fixed Point Theorems for Mixed Monotone Operators and Local Existence-Uniqueness of Positive Solutions for Nonlinear Boundary Value Problems. Journal of Mathematical Analysis and Applications, 382, 594-614. [Google Scholar] [CrossRef] 

为你推荐