Semi-analytical approximations for a class of multi-parameter eigenvalue problems related to tensile buckling

This work complements the first author's recent asymptotic investigations on a class of boundary-eigenvalue problems for tensile buckling of thin elastic plates. In particular, it is shown here that the approximations for the critical buckling load can be improved by using a modified energy method that relies directly on the asymptotic results derived previously. We also explore a number of additional mathematical features that have an intrinsic interest in the context of multi-parameter eigenvalue problems.