Solvability for a class of nonlinear fractional differential equations with parameters

摘要

This paper investigates the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations with parameters. By using the properties of the Green function and Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals of boundary value problem of fractional differential equation are studied and some sufficient conditions for the existence and nonexistence of at least one or two positive solutions for the boundary value problem are obtained. As an application, an example is presented to illustrate the main results.