摘要：In this paper, we consider the properties of the Green’s function for the nonlinear fractional differential equation boundary value problem D 0 + q u ( t ) = f ( t , u ( t ) ) , t ∈ J : = [ 0 , 1 ] , u ( 0 ) = u ′ ( 1 ) = 0 , where 1 < q ≤ 2 is a real number, and D 0 + q is the standard Riemann-Liouville differentiation. As an application of the Green’s function, we give some multiple positive solutions for singular boundary value problems, and we also give the uniqueness of solution for a singular problem by means of the Leray-Schauder nonlinear alternative, a fixed-point theorem on cones, and a mixed monotone method.
关键词：boundary value problem ; fractional differential equations ; Riemann-Liouville fractional derivative ; positive solution ; fixed-point theorem
