Singularly Perturbed Equations with Poles of Different Multiplicities
DOI:
https://doi.org/10.58649/zaa67843Keywords:
singular perturbation, degenerate equation, pole, level lines, asymptotic estimates, successive approximations, limiting transitionAbstract
This paper considers a system of singularly perturbed equations consisting of four first-order equations in a certain domain of the complex plane. The matrix function of the leading approximation has four distinct eigenvalues forming two pairs of complex conjugates. One pair has simple poles, while the other has double poles. The problem of establishing the validity of the limiting transition in a certain subdomain of the region under consideration is formulated. This problem is solved using the method of level lines and successive approximations.
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