Shegda L. Noether boundary-value problems for degenerate systems of ordinary differential equations

Boundary-value problems for degenerate systems of ordinary differential equations are examined under the assumption that the corresponding degenerate linear system of differential equations is transformed to the central canonical form. For the first time the effective coefficient conditions of bifurcation and branching of solutions of weakly excited linear and nonlinear degenerate boundary-value problems are established. The necessary and sufficient conditions for the existence of solutions of the degenerate linear nonhomogeneous boundary-value problem for systems of ordinary differential equations and of weakly nonlinear degenerate systems of ordinary differential equations with Noether linear part in critical are received. The conditions of bifurcation of the solution set of the weakly excited linear degenerate boundary-value problem for systems of ordinary differential equations are discovered on the assumption that the generating problem has no solutions under general multifocal uptake. A method of searching of solutions in the form of Laurent series according to the power of the series expansion parameter with the complete number of negative exponents of has been offered.