We consider a boundary-value problem for a second order singular differential equation and construct a special Banach space with weight where the singular problem becomes regular. Using the notion of upper and lower Nagumo’s function and the Azbelev’s quasilinearization scheme, we proved the theorem of sufficient conditions of existence and unique solvability of solution for a second order quasi-linear singular differential equation.

differential equation, singularity, boundary-value problem.