【摘要】 本文研究一类分数阶微分方程的两点边值问题:{D₀^α+u（t）=-f（t,u（t））,0<t<1,u（0）=u′（0）=u′（1）=0,其中2<α≤3是实数,D₀^α+是标准的Riemann-Liouville微分,f:[0,1]×[0,∞)→[0,∞)是连续函数。本文利用Banach压缩映像原理得到解的唯一性,并在较一般的非紧性测度条件下应用凝聚映射的不动点指数得到该边值问题正解的存在性。更多还原

【Abstract】 In this paper,a class of two-point boundary value problem of fractional differential equations are studied:{D₀^α+u（t）=-f（t,u（t））, 0<t<1,u（0）=u′（0）=u′（1）=0,where 2<α ≤3,D₀^α+is the standard RiemannLiouville fractional derivative.The uniqueness of solution of the fractional two-point boundary value problem is acquired by using Banach’s contraction mapping principle,and the existence of positive solutions for the boundary value problem is obtained by using the fixed point index of the cohesive mapping under the general noncompactness measure condition.更多还原