6 papers
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…
On Scattering by a Cylindrical Trap in Critical Case
Rustem R. Gadyl'shin
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of pole…
On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit
R. Gadyl'shin, Arlen M. Il'in
The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the…
On Local Perturbations of SCHRÖdinger Operator on Plane
R. R. Gadyl'shin
We obtain necessary and sufficient conditions for emerging of small eigenvalue for Schrödinger operator on plane under local operator perturbations. In the case the eigenvalue emer…
On local perturbations of Shrodinger operator in axis
R. R. Gadyl'shin
We adduce the necessary and sufficient condition for arising of eigenvalues of Shrodinger operator in axis under small local perturbations. In the case of eigenvalues arising we co…
Asymptotics of perturbed soliton for Davey--Stewartson II equation
R. R. Gadyl'shin, O. M. Kiselev
It is shown that, under a small perturbation of lump (soliton) for Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution…