Pozur S. Investigation nonlinear singular boundary value problems on a half line for the differential equations of the second order

It was found sufficient conditions for existence of the solution with prescribed numbers of zeros and vanishes at infinity for a rather general differential equation of the second order. For the differential equations of special forms more simple conditions where obtained when above problems have non trivial solutions. As an example it was investigated a boundary value problem for generalized Emden-Fowler’s equation. A perturbed boundary value problems on the half line for a singular nonlinear ordinary differential equation of the second order and singular nonlinear systems of the first and second order differential equations are considered. In each case we find conditions under which solutions of the unperturbed problems are continuous with respect to a small parameter