MATHEMATICS

On eigenvalues of the $n$-dimensional discrete Schrödinger operator with a small decreasing potential

L. E. Morozova

Udmurt State University, Izhevsk

Abstract: 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.

UDC: 517.958:513.145.6

Received: 01.10.2004