Abstract
For the differential equation u ″ = f ( t , u , u ′ ) , where the function f : ( a , b ) × R 2 → R has nonintegrable singularities with respect to the time variable at t = a and t = b , new unimprovable sufficient conditions of solvability and unique solvability of the boundary value problems u ( a ) = 0 , u ( b ) = 0 and u ( a ) = 0 , u ′ ( b ) = 0 are established.
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