Multiplicity of positive solutions of a class of nonlinear fractional differential equations

This paper is concerned with the nonlinear fractional differential equation L(D)u=f(x,u), u(0)=0, 0 0, j = 1,2,…, n − 1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskiiʹs fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer.