Singular perturbation theory for systems of differential equations in the case of multiple spectrum of the limit operator. III

This paper is the third part of work dealing with the construction of a regularized asymptotic expression for the solution of a nonhomogeneous Cauchy problem in a finite-dimensional space $E$. The limit operator has a Jordan structure. On the lines of the theory of branching a method is given for describing all possible singularities of the problem in the case when the structure matrix has degeneracies. As an example, a complete analysis of a Cauchy problem is given in three-dimensional space, along with a certain case in four-dimensional space.
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