Geodesic
Solvability of singular boundary-value problems for ordinary differential equations of order~$2m$
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 174-188

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Theorems on the existence and uniqueness of generalized and classical solutions of the first boundary-value problem for an ordinary differential equation of order $2m$ in the case where the functions involved are nonintegrable at the points at which boundary conditions are imposed (singular problems) are established. The results obtained justify the applicability of the Ritz and Galerkin methods to the problems considered. 
@article{ZNSL_2004_309_a10,
     author = {M. N. Yakovlev},
     title = {Solvability of singular boundary-value problems for ordinary differential equations of order~$2m$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--188},
     publisher = {mathdoc},
     volume = {309},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a10/}
}
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M. N. Yakovlev. Solvability of singular boundary-value problems for ordinary differential equations of order~$2m$. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVII, Tome 309 (2004), pp. 174-188. http://geodesic.mathdoc.fr/item/ZNSL_2004_309_a10/