一类带参数的分数阶微分方程边值问题多个正解的存在性

Existence and multiple positive solutions for a class of fractional differential equation boundary value problem

运用不动点指数理论,作者研究了带参数的分数阶微分方程边值问题{Dα0+u(t)=λf(t,u(t)),0<t<1,u(0)=u(1)=0,烅多个正解的存在性.这里λ>0是一个参数,3<α≤4u′(0)=u′(1)=0是一个实数,Dα0+为标准Riemann-Liouville微分算子.

In this paper, we investigate the existence and nultiplicity of positive solutions for fractional differential equation boundary value problem {D0a＋u（t）=λf（t,u（t））,0〈t〈1,u（0）=u（1）=0,u′（0）=u′（1）=0 where λ〉0 is a parameter, a ∈ R, 3 〈 a ≤ 4. D0a＋ is the standard Riemann-Liouville differential, f： [0,1] × [0,∞）→ [-0,∞） is continuous.