TY - JOUR AU - Shehda, L. M. PY - 2021/01/28 Y2 - 2024/03/29 TI - DEGENERATE BOUNDARY-VALUE PROBLEMS WITH A PERTURBING MATRIX FOR A DERIVATIVE: Array JF - PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number JA - Number VL - IS - 1(59) SE - Mathematics and Mechanics DO - 10.31471/2304-7399-2020-1(59)-29-37 UR - https://pvntsh.nung.edu.ua/index.php/number/article/view/1598 SP - 29-37 AB - <p><em>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.</em><em> 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.</em></p> ER -