Geodesic
Multidimensional discrete Schrödinger equation with limit periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 1, pp. 74-82 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is established that the discrete Schrödinger equation with a small limit periodic potential has a non-trivial solution with the limit periodic modulus for the dense set of the spectrum, which includes the maximal and minimal points. 
@article{TMF_1995_102_1_a7,
     author = {Yu. P. Chuburin},
     title = {Multidimensional discrete {Schr\"odinger} equation with limit periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {74--82},
     year = {1995},
     volume = {102},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a7/}
}
TY  - JOUR
AU  - Yu. P. Chuburin
TI  - Multidimensional discrete Schrödinger equation with limit periodic potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 74
EP  - 82
VL  - 102
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a7/
LA  - ru
ID  - TMF_1995_102_1_a7
ER  - 
%0 Journal Article
%A Yu. P. Chuburin
%T Multidimensional discrete Schrödinger equation with limit periodic potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 74-82
%V 102
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a7/
%G ru
%F TMF_1995_102_1_a7
Yu. P. Chuburin. Multidimensional discrete Schrödinger equation with limit periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 1, pp. 74-82. http://geodesic.mathdoc.fr/item/TMF_1995_102_1_a7/

[1] Kozlov S. M., Tr. Mosk. matem. ob-va, 46, 1983, 99–123 | MR

[2] Tsikon Kh., Freze R., Kirsh V., Saimon B., Operatory Shredingera s prilozheniyami k kvantovoi mekhanike i globalnoi geometrii, Mir, M., 1990 | MR

[3] Chulaevskii V. A., UMN, 36:5 (1981), 203–204 | MR

[4] Avron J., Simon B., Commum. Math. Phys., 82:1 (1981), 101–120 | DOI | MR | Zbl

[5] Lokutsievskaya E. O., TMF, 87:2 (1991), 207–219 | MR | Zbl

[6] Gelfand I. M., DAN SSSR, 73:6 (1950), 1117–1120 | MR | Zbl

[7] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 4, Mir, M., 1982 | MR

[8] Skriganov M. M., Tr. Matem. in-ta AN SSSR, 171, 1985 | MR | Zbl

[9] Shabat B. V., Vvedenie v kompleksnyi analiz, Ch. 2, Nauka, M., 1976 | MR

[10] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[11] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 1, Mir, M., 1977 | MR

[12] Gordon A. Ya., Funkts. analiz i ego prilozh., 20:4 (1986), 70–71 | MR | Zbl