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We consider the problem of the existence of positive solutions u to the problem u (x) = g(u(x)), u(0) = u′(0) = . . . = u(0) = 0 (g ≥ 0, x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition δ\

A singular initial value problem for the equation $u^{(n)}(x) = g(u(x))$