Abstract:
The paper is devoted to the Cauchy problem for a differential equation with a small parameter when using a Fredholm operator in a Banach space with a certain method. The investigated effect of this parameter. The solution is in the form of an asymptotic expansion. When solving the problems of using the cascade decomposition method for equations, which allows us to split the equation into equations in subspaces.
Keywords:
differential equation, asymptotic solution, small parameter, perturbation in the right-hand side, Fredholm operator, boundary layer phenomenon.
Received: 23.04.2018
Bibliographic databases:
Document Type:
Article
UDC:517.928
Language: Russian
Citation:
V. I. Uskov, “Asymptotic solution of first-order equation with small parameter under the derivative with perturbed operator”, Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018), 784–796
\Bibitem{Usk18}
\by V.~I.~Uskov
\paper Asymptotic solution of first-order equation with small parameter under the derivative with perturbed operator
\jour Tambov University Reports. Series: Natural and Technical Sciences
\yr 2018
\vol 23
\issue 124
\pages 784--796
\mathnet{http://mi.mathnet.ru/vtamu22}
\crossref{https://doi.org/10.20310/1810-0198-2018-23-124-784-796}
\elib{https://elibrary.ru/item.asp?id=36239266}
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https://www.mathnet.ru/eng/vtamu22
https://www.mathnet.ru/eng/vtamu/v23/i124/p784
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