Geodesic
On the solvability of a~singular boundary-value problem for the equation $f(t,x,x',x'')=0$
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 10-21

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In this work we consider boundary value problems of the form \begin{gather*} f(t,x,x',x'')=0,\quad 01,\\ x(0)=0,\quad x'(1)=b,\quad b>0, \end{gather*} where the the scalar function $f(t,x,p,q)$ may be singular at $x=0$. As far as we know, the solvability of the singular boundary value problems of this form has not been treated yet. Here we try to fill in this gap. Examples, illustrating our main result, are included. 
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M. K. Grammatikopulos; P. S. Kelevedzhiev; N. I. Popivanov. On the solvability of a~singular boundary-value problem for the equation $f(t,x,x',x'')=0$. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 10-21. http://geodesic.mathdoc.fr/item/CMFD_2006_16_a1/