On solvability and unique solvability of two-point singular boundary value problems

For the differential equation u″=f(t,u,u′),u″=f(t,u,u′), where the function f:(a,b)×R2→Rf:(a,b)×R2→R has nonintegrable singularities with respect to the time variable at t=at=a and t=bt=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.