Sufficient solvability conditions for the boundary value problem for a second order quasilinear singular differential equation

Solvability conditions are obtained for a two-point boundary value problem for a second order quasilinear singular equation. The result is based on the properties of Green's operator of the corresponding semi-homogeneous linear problem. Its boundedness is proved, the upper estimate of its norm is obtained. Solvability conditions for the initial task are obtained from solvability conditions for an equivalent operator equation.