Banach空间中分数阶微分方程边值问题的解
The Solution of Boundary Value Problems for Fractional Differential Equations in Banach Spaces
摘要: 应用不动点定理以及格林函数的性质,在Banach空间中得到了一类带有P-Laplacian算子的分数阶微分方程边值问题解的存在性结果。
Abstract: The existence of solutions for a class of P-Laplacian fractional differential equation boundary value problem is obtained by means of fixed point theorem and the properties of Green function in Banach Space.
文章引用:魏家豪. Banach空间中分数阶微分方程边值问题的解[J]. 理论数学, 2017, 7(2): 78-88. https://doi.org/10.12677/PM.2017.72012

参考文献

[1] Li, C.F. and Luo, X.N. (2010) Existence of Positive Solutions of the Boundary Value Problem for Nonlinear Fractional Differentiial Equations. Computers & Mathematics with Applications, 59, 1363-1375.
https://doi.org/10.1016/j.camwa.2009.06.029
[2] Rehman, M. and Khan, R. (2010) Existence and Uniqueness of Solutions for Multi-Point Boundary Value Problems for Fractional Differential Equations. Applied Mathematics Letters, 23, 1038-1044.
https://doi.org/10.1016/j.aml.2010.04.033
[3] Li, S.J., Liu, L.S., Wiwatanapataphee, B. and Wu, Y.H. (2013) Extremal Solutions for P-Laplacian Differential Systems via Iterative Computation. Applied Mathematics Letters, 26, 1151-1158.
https://doi.org/10.1016/j.aml.2013.06.014
[4] Zhang, C.G., Liu, L.S., Wiwatanapataphee, B. and Wu, Y.H. (2014) The Egenvalue for a Class of Singular P-Laplacian Fractional Differential Equations Involving the Rie-mann-Stieltjes Integral Boundary Conditions. Applied Mathematics and Computation, 235, 412-422.
https://doi.org/10.1016/j.amc.2014.02.062
[5] Wang, J.H. and Xiang, H.J. (2010) Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problem with P-Laplacian Operator. Abstract and Applied Analysis, 2010, Article ID: 971824.
https://doi.org/10.1155/2010/971824
[6] Lu, L.H., Han, Z.L., Sun, S. and Liu, L. (2013) Existence of Positive Solutions for the Boundary Value Problems of Nonlinear Fractional Differential Equations with P-Laplacian. Advances in Difference Equations, 2013, 30.
https://doi.org/10.1186/1687-1847-2013-30
[7] Yang, X., Wei, Z.L. and Dong, W. (2011) Existence of Positive Solutions for the Boundary Value Problem of Nonlinear Fractional Differential Equations. Common Nonlinear Science and Numerical Simulation, 6, 1371-1385.
[8] Aubin, J.P. and Ekeland, I. (1984) Applied Nonlinear Analysis. John Wiley and Sons, New York.