On the buckling eigenvalue problem

Journal of Physics A: Mathematical and Theoretical, 44 (2011), 215-205
http://dx.doi.org/10.1088/1751-8113/44/21/215205

We prove a density result which allows us to justify the application of the method of fundamental solutions to solve the buckling eigenvalue problem of a plate. We address an example of an analytic convex domain for which the first eigenfunction does change the sign and present a large-scale numerical study with polygons providing numerical evidence to some new conjectures.