Multiplicity and Symmetries of the Bifurcation Branching Point in the Square Clamped Plate

摘要

The symmetries of the eigenfunctions corresponding to the first eigenvalue in a square clamped plate are considered by the Weinstein method for intermediate problems. It is shown how this powerful method can be useful in studying a class of bifurcation problems whose prototype is the elastic plate. Knowledge of the eigenfunction symmetries provides a straighforward way to demonstrate the simple multiplicity of the principal bifurcation point by Weyl's lemma.