Positive solutions of singular Dirichlet and periodic boundary value problems

Let A and T be positive numbers. The singular differential equation (r(x)x')' = muq(t)f (t, x) is considered. Here r > 0 on (0, A) may be singular at x = 0, and f (t, x) less than or equal to 0 may be singular at x = 0 and x = A. Effective sufficient conditions imposed on r, mu, q, and f are given for the existence of a solution x to the above equation satisfying either the Dirichlet conditions x(0) = x(T) = 0 or the periodic conditions x(0) = x(T), x'(0) = x'(T), and, in addition, 0 < x < A on (0, T). (C) 2002 Elsevier Science Ltd. All rights reserved.