具有分数阶导数的积分边值问题正解的存在性
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摘要
本文研究一类具有分数阶导数的积分边值问题正解的存在性,利用锥拉伸与压缩不动点定理和Leggett-Williams不动点定理,得到该问题至少存在1个正解和3个正解的存在性条件.并给出两个例子来说明结果的有效性.
The existence of positive solutions is investigated for a class of integral boundary value problems with fractional derivatives by using the fixed point theorem on cone and the Leggett-Williams fixed point theorem.The existence of at least one positive solution and three positive solutions for these problems is obtained.Meanwhile two examples are delivered to illustrate the approach.
The existence of positive solutions is investigated for a class of integral boundary value problems with fractional derivatives by using the fixed point theorem on cone and the Leggett-Williams fixed point theorem.The existence of at least one positive solution and three positive solutions for these problems is obtained.Meanwhile two examples are delivered to illustrate the approach.
引文
[1]白占兵.分数阶微分方程边值问题理论及其应用.北京:中国科学技术出版社,2012(Bai Z B. Theory and application of boundary value problems of fractional differential equations.Beijing:China Science and Technology Press, 2012)
[2]Bai Z B,Lu H S. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Journal of Mathematical Analysis and Applications, 2005, 311(2):495-505
[3]Goodrich C S. Existence of a positive solution to a class of fractional differential equations. J. Applied Mathematics Letters, 2010, 23(9):1050-1055
[4]Zhang S Q. Positive solutions to singular boundary value problem for nonlinear fractional differential equation. J. Computers and Mathematics with Applications, 2010, 59(3):1300-1309
[5]Cabada A, Wang G T. Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J. Journal of Mathematical Analysis and Applications, 2012, 389(1):403-411
[6]Graef J R, Kong L J. Fractional boundary value problems with integral boundary conditions. J.Applicable Analysis, 2013, 93(10):2008-2020
[7]Sun Y P, Zhang X P. Existence and nonexistence of positive solutions of fractional-order two-point boundary value problems. J. Advances in Difference Equations, 2014, 2014:53
[8]Cabada A, Dimitrijevic S, etc. The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions. J. Mathematical Methods in the Applied Sciences,2017, 40(6):1880-1891
[2]Bai Z B,Lu H S. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Journal of Mathematical Analysis and Applications, 2005, 311(2):495-505
[3]Goodrich C S. Existence of a positive solution to a class of fractional differential equations. J. Applied Mathematics Letters, 2010, 23(9):1050-1055
[4]Zhang S Q. Positive solutions to singular boundary value problem for nonlinear fractional differential equation. J. Computers and Mathematics with Applications, 2010, 59(3):1300-1309
[5]Cabada A, Wang G T. Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J. Journal of Mathematical Analysis and Applications, 2012, 389(1):403-411
[6]Graef J R, Kong L J. Fractional boundary value problems with integral boundary conditions. J.Applicable Analysis, 2013, 93(10):2008-2020
[7]Sun Y P, Zhang X P. Existence and nonexistence of positive solutions of fractional-order two-point boundary value problems. J. Advances in Difference Equations, 2014, 2014:53
[8]Cabada A, Dimitrijevic S, etc. The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions. J. Mathematical Methods in the Applied Sciences,2017, 40(6):1880-1891