分数阶微分方程耦合系统共振边值问题解的存在性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1313-1326.

分数阶微分方程耦合系统共振边值问题解的存在性

胡雷^1,2, 张淑琴¹, 侍爱玲³

1.中国矿业大学(北京) 理学院北京 100083|
2.山东交通学院理学院济南 250357|3. 北京建筑大学 |理学院北京 100044

收稿日期:2013-04-23 修回日期:2014-04-06 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11371364)和2013年北京市教委科学技术研究项目(KM201310016001)资助

Existence of |Solutions for Two-point Boundary Value Problem of a Coupled Fractional Differential Equations at Resonance

HU Lei^1,2, ZHANG Shu-Qin¹, SHI Ai-Ling³

1.Department of Mathematics, China University of Mining and Technology, Beijing 100083;
2.School of Science, Shandong Jiaotong University, Shandong Jinan 250357;
3.School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044

Received:2013-04-23 Revised:2014-04-06 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11371364)和2013年北京市教委科学技术研究项目(KM201310016001)资助

摘要/Abstract

摘要：

利用Mawhin迭合度理论, 讨论了共振条件下分数阶微分方程耦合系统两点边值问题解的存在性, 得到了解的存在性和唯一性的充分条件,最后通过一个例子加以说明.

关键词: Mawhin迭合度, 分数阶微分方程, 共振, 两点边值

Abstract:

In this article, we establish the existence results for two-point boundary value problem of a coupled fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results.

Key words: Coincidence degree, Fractional differential equation, Resonance, Two-point boundary conditions

中图分类号:

34B15

胡雷, 张淑琴, 侍爱玲. 分数阶微分方程耦合系统共振边值问题解的存在性[J]. 数学物理学报, 2014, 34(5): 1313-1326.

HU Lei, ZHANG Shu-Qin, SHI Ai-Ling. Existence of |Solutions for Two-point Boundary Value Problem of a Coupled Fractional Differential Equations at Resonance[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1313-1326.

参考文献

[1] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Amsterdam: Elsevier Science B V, 2006

[2] Hilfer R, Ed. Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000

[3] Podlubny I. Fractional Differential Equations. San Diego: Academic Press, 1999

[4] Su X. Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl Math Lett,
2009, 22: 64--69

[5] 王永庆,刘立山. Banach空间中分数阶微分方程$m$点边值问题的正解. 数学物理学报, 2012, 32A: 246--256

[6] Zhang S. Existence of solution for a boundary value problem of fractional order. Acta Mathematica Scientia, 2006, 26: 193--384

[7] Bai Z, L\"{u} H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J Math Anal Appl, 2005, 311: 495--505

[8] Zhang Y, Bai Z, Feng T. Existence results for a coupled system of nonlinear fractional three-point boundary value problems at resonance. Comput Math Appl, 2011, 61(4): 1032--1047

[9] Jiang W. Solvability for a coupled system of fractional differential equations at resonance. Nonlinear Anal, 2012, 13: 2285--2292

[10] Hu Z, Liu W, Chen T. Existence of solutions for a coupled system of fractional differential equations at Resonance. Bound Value Probl, 2012, 98: 1--13

[11] Jiang W. The existence of solutions to boundary value problems of fractional differential equations at resonance. Nonlinear Anal, 2011, 74: 1987--1994

[12] Kosmatov N. Multi-point boundary value problems on an unbounded domain at resonance. Nonlinear Anal, 2008, 68: 2158--2171

[13] Bai Z. Solvability for a class of fractional m-point boundary value problem at resonance. Comput Math Appl, 2011, 62: 1292--1302

[14] Bai Z, Zhang Y. Solvability of fractional three-point boundary value problems with nonlinear growth. Appl Math Comput, 2011, 218(5): 1719--1725

[15] Zhang Y, Bai Z. Existence of solutions for nonlinear fractional three-point boundary value problems at resonance. J Appl Math Comput, 2011, 36: 417--440

[16] Mawhin J. Topological Degree Methods in Nonlinear Boundary Value Problems. NSFCBMS Regional Conference Series in Mathematics. Providence, RI: American Mathematical Society, 1979