非线性分数阶微分方程非奇异边值问题的多重正解

Multiple Positive Solutions for The Nonsingular Boundary Value Problem of A Nonlinear Fractional Differential Equation

通过研究非线性分数阶微分方程边值问题D0＋^α＋u（t）＋f（t，u（t））=0，0〈t〈1 u（0）：u（1）=u’（0）=0的Green函数及其性质，其中2〈α≤3是实数，D缸是标准Riemann—Liouville型微分，利用锥不动点定理证明了非奇异边值问题多重正解的存在性，并举例加以说明．

In this paper, we consider Green＇s function and its properties for the nonlinear fractional differential equation boupdary value problemD0＋^α＋u（t）＋f（t,u（t））=0,0〈t〈1 u（0）：u（1）=u＇（0）=0where 2 〈 a≤ is a real number, and Dα＋ is the standard Riemann-Liouville differentiation. As an application of Green＇s function and its properties, we give some multiple positive solutions for the nonsingular boundary value problem.One concrete example is respectively given to explain the above theorem finally.