Geodesic
Investigation of boundary-value problems for the singular perturbed differential equation of high order
Matematičeskoe modelirovanie, Tome 19 (2007) no. 11, pp. 65-79.

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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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     author = {I. V. Amirkhanov and E. P. Zhidkov and D. Z. Muzafarov and N. R. Sarker and I. Sarhadov and Z. A. Sharipov},
     title = {Investigation of boundary-value problems for the singular perturbed differential equation of high order},
     journal = {Matemati\v{c}eskoe modelirovanie},
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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. Matematičeskoe modelirovanie, Tome 19 (2007) no. 11, pp. 65-79. http://geodesic.mathdoc.fr/item/MM_2007_19_11_a7/

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