摘要：In this paper, we study the existence of multiple positive solutions for the nonlinear fractional differential equation boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 $D^{\alpha}_{0^{+}}u(t)+f(t,u(t))=0 $ , 0 < t < 1 $0< t<1$ , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 $u(0)=u(1)=u'(0)=0$ , where 2 < α ≤ 3 $2<\alpha\leq3$ is a real number, D 0 + α $D^{\alpha}_{0^{+}}$ is the Riemann-Liouville fractional derivative. By the properties of the Green’s function, the lower and upper solution method and the Leggett-Williams fixed point theorem, some new existence criteria are established. As applications, examples are presented to illustrate the main results.
关键词：fractional differential equation ; boundary value problem ; positive solution ; fractional Green’s function ; fixed point theorem ; lower and upper solution method
