Asymptotic solutions of singularly perturbed linear differential-algebraic equations with periodic coefficients

The paper deals with the problem of constructing asymptotic solutions for singular perturbed linear differential-algebraic equations periodic coefficients. case multiple roots a characteristic equation is studied. It assumed that limit pencil matrices system has one eigenvalue multiplicity n, which corresponds to two finite elementary divisors and infinite whose greater than 1.A technique finding developed n formal linearly independent are constructed corresponding system. algorithm nontrivial generalization singularly differential in normal form, was used simple equation.The modification based on equalization method special way coefficients at powers small parameter algebraic systems equations, from expansions searched solution found. Asymptotic estimates terms these respect also given.For an inhomogeneous coefficients, existence uniqueness theorems satisfying some estimate proved, developed. Both critical non-critical cases considered.