We are interested in the existence of solutions to initial-value problems for second-order nonlinear singular differential equations. We show that the existence of a solution can be explained in terms of a more simple initial-value problem. Local existence and uniqueness of solutions are proven under conditions which are considerably weaker than previously known conditions.
"A Singular Initial-Value Problem for Second-Order Differential Equations." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/526549