ON THE LOCATION OF THE LEAST POINT OF THE ESSENTIAL SPECTRUM

D HINTON

hinton@math.utk.edu

Mathematics Department,

University of Tennessee,

Knoxville,

TN 37996-1300, USA

University of Tennessee,

Knoxville,

TN 37996-1300, USA

A new criterion for the least point of the essential spectrum is given
for a one term second order differential operator. This criterion is
sharper than the Friedrich's criterion. Application is given to the
singular eigenvalue problem associated with the buckling of a column
under self-weight subjected to the constraint of fixed volume. Examples
are given which illustrate the sharpness of the bounds for the least
point of the essential spectrum.

EPSRC Gregynog Workshop, 21-26 July 2002