Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1121-1131
We study the relaxed elastic line in a more general case on an oriented surface. In particular, we obtain a differential equation with three boundary conditions for the generalized relaxed elastic line. Then we analyze the results in a plane, on a sphere, on a cylinder, and on the geodesics of these surfaces.
Direct and inverse problems for the Dirac operator with a spectral parameter linearly contained in a boundary condition
Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1155-1166
We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse spectral problem with known collection of eigenvalues and normalizing constants or two spectra.