A criterion for the unique solvability of and sufficient conditions for the correctness of the modified Vallèe-Poussin problem are established for the linear ordinary differential equations with singularities.
@article{107506, author = {G. D. Tskhovrebadze}, title = {On a multipoint boundary value problem for linear ordinary differential equations with singularities}, journal = {Archivum Mathematicum}, volume = {030}, year = {1994}, pages = {171-206}, zbl = {0815.34013}, mrnumber = {1308353}, language = {en}, url = {http://dml.mathdoc.fr/item/107506} }
Tskhovrebadze, G. D. On a multipoint boundary value problem for linear ordinary differential equations with singularities. Archivum Mathematicum, Tome 030 (1994) pp. 171-206. http://gdmltest.u-ga.fr/item/107506/
Sur l’equation differentielle lineaire du second ordre., Determination d’une integrale par deux valeurs assignees. Extension aux equation d’ordre $n$. J. Math. pures et appl. (1929) 8, No. 2, 125-144.
On a singular multi-point boundary value problem, Ann. Math. pura ed appl. 86 (1970), 367-400. (1970) | MR 0271449 | Zbl 0251.34012
Some singular boundary value problems for ordinary differential equations, Tbilisi: Izd-vo Tbilisskogo Univ. (1975), 352. (in Russian) (1975) | MR 0499402
The boundary value problems for systems of ordinary differential equations, (Itogi nauki i tekhniki. VINITI AN SSSR), Sovremennie problemi matematiki. Noveishie dostijenia T. 30 (1987), 3-103. (in Russian) (1987) | MR 0925829
On some estimates of Green’s functions for multipoint boundary value problem, Mat. zametki 4 No. 5 (1968), 533-540. (in Russian) (1968)
On a singular boundary value problem of the Vallèe Poussin’s type, Trudy Inst. Prikl. Math. Tbilisskogo Univ. 31 (1988), 179-194. (in Russian) (1988) | MR 1001347
Green’s function inequalities for two point boundary value problem, Pacif. J. Math. 59, No. 2 (1975), 327-343. (1975) | MR 0437841