Abstract
In this paper, we investigate the existence of positive solutions for the following nonlinear fractional semipositone boundary value problem :
D(0+)(alpha)u(t) = -f(t, u), 0 < t < 1, 1 < alpha <= 2,
u(0) = 0, u(1) = beta u(eta),
where D-0+(alpha) is the standard Riemann-Liouville differential operator of order alpha, and the nonlinear term f : (0,1] x (0, +infinity) -> (-infinity, +infinity) satisfies Caratheodory Condition and we also allow that the nonlinear term f is both semipositone and lower unbounded. By using the fixed point theorem in a cone, the existence of many positive solutions are obtained.