Abstract
In this work, we consider the following nonlinear fractional differential equation -D nu u(t)=lambda f(t,u(t))+e(t)in(0,1),u(j)(0)=0,0 <= j <= n-2,[D alpha u(t)]t=1=0,where lambda>0 is a parameter, n >= 3 n-1<nu<n 1 <=alpha <= n-2 and D nu stands for the standard Reimann-Liouville derivative, f:[0,1]x[0,+infinity)& x27f6;R is sign-changing continuous function (that is, we have a so-called equation of semipositone problems). The perturbed term e:(0,1)-> R is measurable function and verifies some appropriate conditions. We derive some intervals of lambda such that the problem has positive solutions. Our study relies on Guo-Krasnoselskii fixed point theorem.