Geodesic
Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm–Liouville type
Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 359-368 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a non-linear eigenvalue problem similar to a linear Sturm–Liouville problem the properties of the spectrum and the eigenfunctions are analysed. The system of eigenfunctions is shown to be a Riesz basis in $L_2$. 
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P. E. Zhidkov. Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm–Liouville type. Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 359-368. http://geodesic.mathdoc.fr/item/SM_2000_191_3_a3/

[1] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976 | MR

[2] Zhidkov P. E., “O polnote sistem sobstvennykh funktsii operatora Shturma–Liuvillya s potentsialom, zavisyaschim ot spektralnogo parametra, i nekotoroi nelineinoi zadachi”, Matem. sb., 188:7 (1997), 123–138 | MR | Zbl

[3] Zhidkov P. E., Eigenfunction expansions associated with a nonlinear Schrödinger equation, Joint Inst. Nuclear Research Comm. E5-98-61, Dubna, 1998 | MR

[4] Bari N. K., “O bazisakh v gilbertovom prostranstve”, Dokl. AN SSSR, 54:5 (1946), 383–386 | MR

[5] Bari N. K., “Biortogonalnye sistemy i bazisy v gilbertovom prostranstve”, Uchenye zapiski MGU. Matematika, 148 (1951), 69–107 | MR

[6] Guter R. S., Ulyanov P. L., “O novykh rezultatakh v teorii ortogonalnykh ryadov”, Dopolnenie v knige: Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, Gos. izd. fiz.-mat. lit-ry, M., 1958 | MR

[7] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[8] Makhmudov A. P., Osnovy nelineinogo spektralnogo analiza, Izd-vo Azerbaidzhanskogo gos. un-ta im. S. M. Kirova, Baku, 1984 | MR

[9] Levitan B. M., Sargsyan I. S., Operatory Shturma–Liuvillya i Diraka, Nauka, M., 1988 | MR | Zbl

[10] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR