## On the asymptotic behavior of the discrete spectrum in buckling
problems for thin plates

*
Monique Dauge,
Manil Suri
*

We consider the buckling problem for a family of thin plates with
thickness parameter **epsilon**. This
involves finding the least positive multiple
**L**_{min}(epsilon)
of the
load that makes the plate *buckle*, a value
that can be expressed in terms of an eigenvalue
problem involving a non-compact operator. We show that under
certain assumptions on the load, we have

**L**_{min}(epsilon) = O(epsilon^{2})
This guarantees
that provided the plate is thin enough, this minimum value can be
numerically approximated without the spectral
pollution that is possible due to the presence of the non-compact
operator. We provide numerical
computations illustrating some of our theoretical results.
This paper completes the analysis dome in the
Previous Paper.

Rennes, Baltimore, July 2004.

Preprint Rennes 04-39

*Math. Meth. Appl. Sc.* **Vol. 29, 2006**, pp 789-817.