On the asymptotic behavior of the discrete spectrum in
buckling
problems for thin plates
Monique Dauge and Manil Suri
We consider the buckling problem for a family of thin plates with
thickness parameter $\varepsilon$. This
involves finding the least positive multiple $\lambda_{\min}^\varepsilon$
of the
load that makes the plate {\em 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
$\lambda_{\min}^\varepsilon = {\cal O}(\varepsilon^2)$. 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.