Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order

We investigate the existence of nontrivial solutions for a multi-point boundary value prob- lem for fractional differential equations. Under certain growth conditions on the nonlin- earity, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray Schauder nonlinear alternative. As an application, some examples to illustrate our results are given.