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 Matem. Mod., 2007, Volume 19, Number 11, Pages 65–79 (Mi mm1213)

Investigation of boundary-value problems for the singular perturbed differential equation of high order

I. V. Amirkhanov, E. P. Zhidkov, D. Z. Muzafarov, N. R. Sarker, I. Sarhadov, Z. A. Sharipov

Joint Institute for Nuclear Research

Abstract: By the different methods the boundary-value problems for the differential equations of high order with the small parameter $\varepsilon$ at higher derivatives are investigated. A comparative analysis of the obtained results is given at diminution of $\varepsilon$. The existence of a boundary layer for a derivative from the solutions is established. It is shown, that at diminution of $\varepsilon$ the solutions of one boundary-value problem (when for the solution $\psi(r)$ of the given equation sets the next boundary conditions: $\psi(0)=0$, $\psi"(0)=0$, $\psi^{\mathrm{IV}}(0)=0$, $\cdots$; $\psi(\infty)=0$) converge to the solutions of a degenerate problem (Schrödinger equation), and for the other (when the boundary conditions are given by: $\psi(0)=0$, $\psi'(0)=0$, $\psi"(0)=0$, $\cdots$; $\psi(\infty)=0$) such convergence doesn't exist.

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Citation: I. V. Amirkhanov, E. P. Zhidkov, D. Z. Muzafarov, N. R. Sarker, I. Sarhadov, Z. A. Sharipov, “Investigation of boundary-value problems for the singular perturbed differential equation of high order”, Matem. Mod., 19:11 (2007), 65–79

Citation in format AMSBIB
\Bibitem{AmiZhiMuz07} \by I.~V.~Amirkhanov, E.~P.~Zhidkov, D.~Z.~Muzafarov, N.~R.~Sarker, I.~Sarhadov, Z.~A.~Sharipov \paper Investigation of boundary-value problems for the singular perturbed differential equation of high order \jour Matem. Mod. \yr 2007 \vol 19 \issue 11 \pages 65--79 \mathnet{http://mi.mathnet.ru/mm1213} \zmath{https://zbmath.org/?q=an:1140.65338} \elib{http://elibrary.ru/item.asp?id=9601484}