一类分数阶微分方程边值问题解的存在性

Existence of positive solutions for boundary value problem of fractional differential equations

利用Krasnoselskiis不动点定理,研究非线性分数阶微分方程D0α+u(t)=λa(t)f(t,u(t),u'(t)),0<t<1,u(0)+u″(0)=0,u(1)+u″(1)=0,u'(0)=0特征值取值范围,得到问题解的存在性和不存在性的充分条件,其中2<α≤3是一个实数,并且D0α+是Caputo型微分。

This paper describes the use of Krasnoselskiis fixed point theorem for study on the eigenvalue intervals of this fractional differential equation Dα0＋u（t）=λa（t）f（t,u（t）,u′（t））,0t1 u（0）＋u″（0）=0,u（1）＋u″（1）=0,u′（0）=0 Where 2α≤3 is a real number,and Dα0＋ is a Caputo′s differentiation.The existence and nonexistence of positive solutions for the fractional boundary value problem are obtained.