Positive solutions of singular positone dirichlet boundary value problems

The singular Dirichlet boundary value problem x″ + μq(t)f(t,x,x′) = 0, x(0) = x(T) = 0 is considered. Here f(t,x,y) ≥ 0 may be singular at x = 0 and x = A > 0 of the phase variable x and at y = 0 of the phase variable y. Effective sufficient conditions imposed upon μ, q, and f are given for the solvability of the above problem in the set {x : x ∈ C1(J) ∩ C2((0,T) β t : t ∈ [0,T], x′(t) = 0}), 0 < x(t) < A, for t ∈ (0,T)}.