中文摘要：

考虑分数阶半正边值问题：Dα0＋u（t）=λf（t,u（t））,0〈t〈1,u（0）=u（1）=u′（0）=u′（1）=0正解的存在性.其中：3〈α≤4是一个实数;Dα0＋是标准的Riemann-Liouville微分,非线性项没有数值下界.应用Krasnosel’skii不动点定理证明该方程一个正解的存在性.

英文摘要：

We studied a positive solution of the semipositone boundary value problem of fractional differential equation：Dα0＋u（t）=λf（t,u（t））, 0t1,u（0）=u（1）=u′（0）=u′（1）=0,where 3α≤4is a real number,and Dα0＋is the standard Riemann-Liouville differentiation,and the nonlinear term has no numerical lower bound.We gave an existence theorem of this equation by means of the Krasnosel＇skii fixed-point theorem on a cone.