83 citations · 248 across the 13 of their papers we have counts for
13 papers
On quantum waveguide with shrinking potential
A. Bikmetov, R. Gadyl'shin
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from th…
Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case
Youcef Amirat, Gregory A. Chechkin, Rustem R. Gadyl'shin
We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue o…
On spectrum of a periodic operator with a small localized perturbation
D. Borisov, R. Gadyl'shin
We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independe…
On spectrum of a Schroedinger operator with a fast oscillating compactly supported potential
Denis I. Borisov, Rustem R. Gadyl'shin
We study the phenomenon of an eigenvalue emerging from essential spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential. We prove the suf…
On regular and singular perturbations of acoustic and quantum waveguides
Rustem R. Gadyl'shin
We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in -dimensional cylinders. Existence of eigenvalue…
On Boundary -- Value Problems for the Laplacian in Boundedand in Unbounded Domains Withperforated Boundaries
Gregory A. Chechkin, Rustem R. Gadyl'shin
In the paper we consider boundary -- value problems with rapidly alternating type of boundary conditions, including problems in domains with perforated boundaries. We present the c…