Open AccessDEGENERATE BOUNDARY-VALUE PROBLEMS WITH A PERTURBING MATRIX FOR A DERIVATIVE
Author(s) -
L. M. Shehda
Publication year - 2021
Publication title -
prikarpatsʹkij vìsnik ntš. čislo
Language(s) - English
Resource type - Journals
ISSN - 2304-7399
DOI - 10.31471/2304-7399-2020-1(59)-29-37
Subject(s) - mathematics , boundary value problem , mathematical analysis , noether's theorem , boundary (topology) , degenerate energy levels , mixed boundary condition , matrix (chemical analysis) , laurent series , physics , materials science , quantum mechanics , lagrangian , composite material
In the paper, there is considered degenerated Noether boundary value problem with a perturbing matrix for a derivative, in which the boundary condition is given by a linear vector functional. We have proposed an algorithm to consrtuct a set of linearly independent solutions of boundary value problems with a small parameter in the general case, when the number of boundary conditions given by a linear vector functional does not match with the number of unknowns in a degenerate differential system. There is used the technique of pseudoinverse Moore-Penrose matrices. Applying the Vishik-Lyusternik method, the solution of the boundary value problem is obtained as part of the Laurent series in powers of small parameter. We obtain conditions for the bifurcation of solutions of linear degenerated Noether boundary-value problems with a small parameter under the assumption that the unperturbed degenerated differential system can be reduced to central canonical form.