Abstract
Eigenvalue problems for the biharmonic operator (iterated Laplacian)L= ΔΔ will be studied on bounded plane domains. Our purpose is to obtain asymptotic variational formulae for eigenvalues and eigenfunctions under the deformation of removing an ∊-disk and adjoining additional boundary conditions on the new boundary component thereby introduced, valid on a positive interval 0 < ∊ < ∊0. Eigenvalue problems can be considered in connection with each of the following sets of homogeneous boundary conditions.
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