Perturbing a rectangular membrane with a restorative force: effects on eigenbvalues and eigenfunctions.
Arturo Portnoy · Communications in Partial Differential Equations · 1998
Series expansions are obtained for a rich subset of eigenvalues and eigenfunctions of an operator that arises in the study of rectangular membranes: the operator is the 2-D Laplacian with restorative force term and Dirichlet boundary conditions. Expansions are extracted by considering the restorative force term as a linear perturbation of the Laplacian; errors of truncation for these expansions are estimated. Theriteria defining the subset of eigenvalues and eigenfunctions that can be studied depends only on the size and linearity of the perturbation. The results are valid for almost all rectangular domains.