Akymenko A. Periodic solutions of a singular disturbed system of differential equations

This dissertation research deals with the finding of existence and uniqueness conditions for the periodic solution of the system and construction of its asymptotics in different cases of boundary-bundles matrices spectrum behavior as well as the finding of conditions for the above systems solutions stability. Stability conditions for the solutions of singular disturbed systems of differential equations with periodic coefficients in the case of their reduction to the central canonical form are found in this work. A necessary and sufficient conditions for existence of a periodic solution of the singular disturbed system of differential equations in the critical case are found as well. Asymptotics formulas for fundamental matrix, monodromy matrix, and multipliers of the singular disturbed system of the first and second order in different cases of the boundary-bundles matrices spectrum behavior are deduced. Sufficient conditions for the system stability and the existence of its unique periodic solution areobtained. The asymptotics formula of the periodic solutions of the singular disturbed system of the first or second orders differential equations with periodic coefficients is constructed under the existence and uniqueness conditions for the solutions.