Geodesic
Regularity of self-adjoint boundary conditions
Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 835-846

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It is shown that self-adjoint boundary conditions for ordinary differential operators of odd order are regular in Birkhoff's sense. A similar result, for differential operators of even order, was proved by a different method by Salaff. In short, Kamke's hypothesis about the regularity of self-adjoint boundary conditions is completely confirmed. 
@article{MZM_1977_22_6_a5,
     author = {A. M. Minkin},
     title = {Regularity of self-adjoint boundary conditions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {835--846},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a5/}
}
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A. M. Minkin. Regularity of self-adjoint boundary conditions. Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 835-846. http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a5/