The first eigenvalue of the Laplace operator

Baltabek Esmatovich Kanguzhin, Dostilek Dauitbek

2016

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DOI 10.1063/1.4959744
Data confidence 70 medium
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Abstract

We consider a self-adjoint differential operator in the Hilbert space. The domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “there are no eigenvalues on neighborhood of zero” from the points of the spectrum of the perturbed operator. For the Sturm-Liouville operator on the segment and the Laplace operator on the square such a possibility is achieved through integral perturbations of boundary conditions. These statements are given with full proofs, and with a possible extension.