Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter

In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions:D"0"+^@au(t)+h(t)f(t,u(t))=0,0

[1]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[2]  J. Webb,et al.  Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type , 2006 .

[3]  R. Cameron,et al.  Nonlinear Integral Equations , 1964 .

[4]  Zhanbing Bai,et al.  Existence of positive solution for singular fractional differential equation , 2009, Appl. Math. Comput..

[5]  Tingting Qiu,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation. , 2008 .

[6]  Xiaoling Han,et al.  Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition , 2011 .

[7]  Hussein A. H. Salem,et al.  On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies , 2009 .

[8]  R. Kress.  Linear Integral Equations , 1989 .

[9]  Zhanbing Bai,et al.  On positive solutions of a nonlocal fractional boundary value problem , 2010 .

[10]  Hui Fang,et al.  Multiple periodic solutions for a discrete time model of plankton allelopathy , 2006 .

[11]  K. Deimling.  Nonlinear functional analysis , 1985 .

[12]  Joe S. Wang.  DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE , 2011, 1108.4463.

[13]  Leo F. Boron,et al.  Positive solutions of operator equations , 1964 .

[14]  Weigao Ge,et al.  Positive solutions for fractional four-point boundary value problems☆ , 2011 .

[15]  D. Jiang,et al.  The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application , 2010 .

[16]  C. F. Li,et al.  Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations , 2010, Comput. Math. Appl..

[17]  B. Liu,et al.  Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems , 2010 .

[18]  Daqing Jiang,et al.  Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation , 2009 .

[19]  J. Webb,et al.  Semi-positone nonlocal boundary value problems of arbitrary order , 2009 .

[20]  Sihua Liang,et al.  Positive solutions for boundary value problems of nonlinear fractional differential equation , 2009 .

[21]  Lishan Liu,et al.  Positive solutions for a nonlocal fractional differential equation , 2011 .

[22]  Haibo Chen,et al.  Unique positive solutions for fractional differential equation boundary value problems , 2010, Appl. Math. Lett..

[23]  M. El-shahed,et al.  Existence of Positive Solutions of the Boundary Value Problem for Nonlinear Fractional Differential Equations , 2011 .

[24]  Xiaojie Xu,et al.  Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations , 2011 .

[25]  Yige Zhao,et al.  Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations , 2011 .

[26]  Wei Dong,et al.  Uniqueness of positive solutions for a class of fractional boundary value problems , 2012, Appl. Math. Lett..

[27]  S. Stank.  The existence of positive solutions of singular fractional boundary value problems , 2011 .

[28]  Christopher S. Goodrich,et al.  Existence of a positive solution to a class of fractional differential equations , 2010, Appl. Math. Lett..

[29]  D. O’Regan,et al.  Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations , 2010 .

[30]  Gennaro Infante,et al.  Non‐local boundary value problems of arbitrary order , 2009 .

[31]  Yige Zhao,et al.  The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations , 2011 .

[32]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

[33]  Ravi P. Agarwal,et al.  Positive solutions for mixed problems of singular fractional differential equations , 2012 .

[34]  Nickolai Kosmatov,et al.  A singular boundary value problem for nonlinear differential equations of fractional order , 2009 .

[35]  Hossein Jafari,et al.  Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method , 2006, Appl. Math. Comput..

[36]  Chuanzhi Bai,et al.  Triple positive solutions for a boundary value problem of nonlinear fractional differential equation , 2008 .

[37]  Moustafa El-Shahed,et al.  Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation , 2007 .

[38]  Chengjun Yuan,et al.  Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations , 2010 .