Criteria for the existence and uniqueness of a solution of the boundary value problem
are established, where ƒ :]a, b[×R2 → R satisfies the local Carathéodory conditions, and μ : [a, b] → R is the function of bounded variation. These criteria apply to the case where the function ƒ has nonintegrable singularities in the first argument at the points a and b.
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