Geodesic
On the solvability of a boundary-value problem for a second-order singular quasilinear equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 91-94.

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We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of the existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.
Keywords: singular ordinary differential equation, boundary-value problem, Green operator, quasilinear equation. 
@article{INTO_2017_132_a20,
     author = {V. P. Plaksina and I. M. Plaksina and \`E. V. Plekhova},
     title = {On the solvability of a boundary-value problem for a second-order singular quasilinear equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {91--94},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a20/}
}
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V. P. Plaksina; I. M. Plaksina; È. V. Plekhova. On the solvability of a boundary-value problem for a second-order singular quasilinear equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 91-94. http://geodesic.mathdoc.fr/item/INTO_2017_132_a20/