Geodesic
A maximum of the first eigenvalue of semibounded differential operator with a parameter
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 14-21.

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We consider a self-adjoint differential operator in Hilbert space. Then the domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “is cleared” 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 attained cia integral perturbations of boundary conditions.
Keywords: Laplace operator, eigenfunction, eigenvalue. 
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B. E. Kanguzhin; D. Dauitbek. A maximum of the first eigenvalue of semibounded differential operator with a parameter. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 14-21. http://geodesic.mathdoc.fr/item/IVM_2017_2_a1/

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