Solutions for a nonlinear fractional boundary value problem with sign-changing Greens function

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a uniqueness result. Moreover, the existence result of positive solutions is obtained when the nonlinear term is also allowed to change sign.