非线性分数阶微分方程边值问题正解的存在性

Existence of Positive Solutions for Boundary Value Problems with Nonlinear Fractional Differential Equations

该文研究了下面分数阶微分方程边值问题格林函数的相关性质D0＋αu（t）=f（t,u（t））,0〈t〈1,u（0）=u（1）=u′（0）=u′（1）=0,其中3〈α≤4是实数,D0＋α是标准的Riemann-Liouville微分,f：[0,1]×[0,∞）→[0,∞）连续.应用格林函数的性质构造了锥,从而应用一些不动点定理得到了正解的存在性.

In this paper,the authors consider the properties of Green’s function for the nonlinear fractional differential equation boundary-value problem D0＋αu（t）=f（t,u（t））,0〈t〈1, u（0）=u（1）=u’（0）=u’（1）=0, where 3〈α≤4 is a real number,and D0＋αis the standard Riemann-Liouville differentiation, and f：[0,1]×[0.∞）→[0,∞）is continuous.As an application of Green’s function,the authors give some multiple positive solutions for nonlinear by means of some fixed-point theorem on cones.