in which the functions r, p and q are continuous on (0, oo) while r is positive there. The point x=O is singular for the functional in the sense that the conditions on r, p, and q may not hold for an interval of the form [0, b]. Finally, all integrals which appear are Lebesgue integrals. We denote by: F[O, b], the class of all functions y such that y is absolutely continuous and y'CL2 on every closed subinterval of (0, b] while y(b) =0; F' [0, b], the class of all functions y such that y F[0, b] and y is bounded on [0, b]; Fo[o[ b], the class of all y F[0, b] for which the point x=0 is a limit point of zeros of y; A [0, b], the class of all yCF[0, b] for which y is continuous on [0, b] and for which y(O) =0; Ao[0, b), the class of all yCA [0, b] for which the point x = 0 is a limit point of zeros of y. For a function y in any one of the above classes J(yY) b exists as a Lebesgue integral and is finite for 0