Geodesic
On eigenvalues of the $n$-dimensional discrete Schr\"odinger operator with a small decreasing potential
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 115-122

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the n-dimensional discrete Schrödinger operator with a decreasing small potential. We prove that there is eigenvalue of this operator close to each of the points $\pm 4$ — this is the boundary of the essential spectrum — when $n=2$ and potential is non-negative (or non-positive). When $n>2$ there are no eigenvalues of this operator. 
@article{VUU_2005_1_a7,
     author = {L. E. Morozova},
     title = {On eigenvalues of the $n$-dimensional discrete {Schr\"odinger} operator with a small decreasing potential},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {115--122},
     publisher = {mathdoc},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2005_1_a7/}
}
TY  - JOUR
AU  - L. E. Morozova
TI  - On eigenvalues of the $n$-dimensional discrete Schr\"odinger operator with a small decreasing potential
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2005
SP  - 115
EP  - 122
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2005_1_a7/
LA  - ru
ID  - VUU_2005_1_a7
ER  - 
%0 Journal Article
%A L. E. Morozova
%T On eigenvalues of the $n$-dimensional discrete Schr\"odinger operator with a small decreasing potential
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2005
%P 115-122
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2005_1_a7/
%G ru
%F VUU_2005_1_a7
L. E. Morozova. On eigenvalues of the $n$-dimensional discrete Schr\"odinger operator with a small decreasing potential. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 115-122. http://geodesic.mathdoc.fr/item/VUU_2005_1_a7/