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

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By using the theory of polynomial matrix pencils, we construct the asymptotics of linearly independent solutions of homogeneous singularly perturbed system of linear differential equations of any order m with matrices at higher derivatives degenerating as a small parameter approaches zero. The general case is analyzed. In this case, the limit matrix pencil has several finite and infinite elementary divisors of both the same and different multiplicities. The corresponding asymptotic estimates are presented.

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References

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  1. Drahomanov National Pedagogic University, Pyrohov Str., 9, Kyiv, 01030, Ukraine

    S. P. Pafyk

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  1. S. P. Pafyk
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Correspondence to S. P. Pafyk.

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Translated from Neliniini Kolyvannya, Vol. 21, No. 3, pp. 368–396, July–September, 2018.

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Pafyk, S.P. Asymptotics of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations. J Math Sci 243, 433–466 (2019). https://doi.org/10.1007/s10958-019-04549-7

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  • DOI: https://doi.org/10.1007/s10958-019-04549-7

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