IMPULSE BOUNDARY VALUE PROBLEM WITH DEGENERATED MATRIX AT DERIVATIVE - Shehda, L. M. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
The article considers a degenerate impulse boundary value problem for systems of ordinary differential equations with a matrix degenerate on the entire segment where the problem is considered, with respect to the derivative, for the case when the number of unknowns does not coincide with the number of boundary conditions. A criterion for the existence of solutions to a degenerate impulse boundary value problem is obtained, assuming that the degenerate differential system reduces to the central canonical form. For the problem under consideration, the conditions for the existence of solutions to a degenerate impulse boundary value problem are reduced to the solution of the algebraic system.