Asymptotic Analysis of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations

Abstract

We consider a homogeneous system of linear singularly perturbed differential equations of order m with matrix at higher derivatives that becomes singular as the small parameter approaches zero. By using the Newton diagrams, we study the structure of the general solution of the analyzed system and the possibility of construction of its asymptotics in the case where the corresponding characteristic polynomial of the matrix has multiple finite and infinite elementary divisors. The obtained results generalize the results obtained for similar systems of equations of the first and second orders.