PDF(288 KB)
PDF(288 KB)
PDF(288 KB)
一类带p-Laplacian算子分数阶微分方程边值问题的正解
Positive Solutions for Boundary Value Problem of Fraction Differential Equations with p-Laplacian Operator
本文应用凸锥上的不动点定理， 讨论了一类带p-Laplacian算子分数阶微分方程边值问题的正解的存在性， 分别得到了这类边值问题至少存在一个正解和多个正解的充分条件. 最后， 给出了两个具体的例子.
In this paper, we consider the existence and the multiplicity of positive solution for boundary value problem of fractional differential equations with p-Laplacian operator. By using some fixed-point theorems on a convex cone, the existence and the multiplicity results of positive solution are obtained.
分数阶微分方程 / 边值问题 / p-Laplacian算子 / 正解 {{custom_keyword}} /
fractional differential equation / boundary value problem / p-Laplacian operator / positive solution {{custom_keyword}} /
[1] Benchohra M, Henderson J, Ntouyas S K. Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl., 2008, 338: 1340-1350 (2008)
[2] Lin W. Global existence theory and chaos control of fractional differential equations. J. Math. Anal. Appl., 2007, 332: 709-726
[3] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., Amsterdam, 2006
[4] N'Guerekata G M. A Cauchy problem for some fractional abstract differential equation with non local conditions. Nonlinear Anal., 2009, 70: 1873-1876 (2009)
[5] Podlubny I. Fractional Differential Equations. Academic Press, San Diego, 1999
[6] Vasundhara J, Lakshmikantham V. Nonsmooth analysis and fractional differential equations. Nonlinear Anal., 2009, 70: 4151-4157
[7] Salem H A H. On the nonlinear Hammerstein integral equations in Banach spaces and application to the boundary value problem of fractional order. Math. Comp. Mode., 2009, 70: 1873-1876
[8] Salem H A H. On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies. J. Comp. Appl. Math., 2009, 224: 567-572
[9] Su X. Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett., 2009, 22: 64-69
[10] Tian Y, Bai Z. Existence results for the three-point impulsive boundary value problem involving fractional differential equations. Comp. Math. Appl., 2010, 59: 2601-2609
[11] Tian Y, Chen A. The existence of positive solution to three-point singular boundary value problem of fractional differential equation. Abst. Appl. Anal., Vol.2009, Article ID 314656, 18 pages, 2009
[12] Tian, Y. Positive solutions to m-point boundary value problem of fractional differential equation. Acta Math. Appl. Sinica (English Series), 2013, 29: 661-672
[13] Wang Y, Liu L, Wu Y. Positive solutions for a class of fractional boundary problem with changing sign nonlinearity. Nonlinear Anal., 2011, 74: 6434-6441
[14] Zhou Y, Tian Y, He Y. Floquet Boundary Value Problem of fractional differential equation. Electron. J. Qualitative Theory Diff. Equ., 2010, 50: 1-13
[15] Feng H, Pang H, Ge W. Multiplicity of symmetric Positive solutions for a multipoint boundary problem with a one-dimensional p-Laplacian. Nonlinear Anal., 2008, 69: 3050-3059
[16] Su H, Wei Z, Wang B. The existence of positive solutions for a nonlinear four-point singular boundary value problem with a p-Laplacian operator. Nonlinear Anal., 2007, 66: 2204-2217
[17] Tian Y, Chen A, Ge W. Multiple positive solutions to multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects. Czech. Math. Jour., 2011, 61: 127-144
[18] Wang Y, Hou C. Existence of multiple positive solutions for one dimensional p-Laplacian. J. Math. Anal. Appl., 2006, 315: 144-153
[19] Zhang, X., Ge, W. Impulsive boundary value problems involving the one-dimensional p-Laplacian. Nonlinear Anal., 2009, 70: 1692-1701
[20] Krasnosel'skii M A. Positive Solutions of Operator Equations. Noordhoff, Groningen, 1964
[21] Leggett R W, Williams L R. Multiple positive fixed points of nonliear operators on ordered Banach spaces. Indiana Univ. Math. J., 1979, 28: 673-688
湖南省重点建设学科，湖南省自然科学基金（2015JJ6101）项目资助.
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