Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2005), pp. 115-122
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L. E. Morozova. On eigenvalues of the $n$-dimensional discrete Schrödinger 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/
@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},
year = {2005},
number = {1},
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 Schrödinger operator with a small decreasing potential
JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY - 2005
SP - 115
EP - 122
IS - 1
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 Schrödinger operator with a small decreasing potential
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2005
%P 115-122
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2005_1_a7/
%G ru
%F VUU_2005_1_a7
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.
