Potorocha V. The asymptotic solutions for degenerated singulary perturbed systems of the differential equations with pulses

Thesis is devoted to solving the problem on constructing asymptotic solutions for the degenerated singulary per-turbed non-linear systems of differential equations with pulses at the fixed time moments. Algorithm of constructing asymptotic solutions of the problem mentioned above is developed on the base of boundary function technique. To construct asymptotic solution in exact form we formulate the corresponding Cauchy problems, its solvability and lemmas on proper-ties of boundary functions which the asymptotic solu-tions consist of are proved. The justification of the pro-posed algorithm is given and the corresponding theorems on estimation of difference between exact and approxi-mated solutions are proved.