Abstract
The boundary value problem
D(alpha)u(t) + mu a(t)f(t,u(t) - q(t) = 0,
u(0) = u'(0) = ... = u((n-2)) (0) = 0, u(1) = lambda integral(1)(0) u(s)ds
is studied, where mu is a positive parameter, f : [0; 1] x [0; + infinity) ! [0; + infinity) and a : (0; 1) ! [0; + infinity) are continuous functions, while q : (0; 1) -> [0; + infinity) is a measurable function. The case, where the function a has singularities at the points t = 0 and t = 1, is admissible.
Conditions are found guaranteeing, respectively, the existence of at least one and at least two positive solutions. Examples are gives.