We adduce the necessary and sufficient condition for arising of eigenvalues of ShrÃ¶dinger operator in axis under small local perturbations. In the case of eigenvalues arising we construct theirâ€¦ (More)

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 perturbed problemâ€¦ (More)

In this papet we consider an acoustic resonator withfmite thickness of the shell and with the Neumann boundaiy condition The extenor and the intenor of the resonator are connected by a thin tube Weâ€¦ (More)