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Reduction from a Semi-Infinite Interval to a Finite Interval of a Nonlinear Boundary Value Problem for a System of Second-Order Equations with a Small Parameter

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Abstract

We consider a boundary value problem over a semi-infinite interval for a nonlinear autonomous system of second-order ordinary differential equations with a small parameter at the leading derivatives. We impose certain constraints on the Jacobian under which a solution to the problem exists and is unique. To transfer the boundary condition from infinity, we use the well-known approach that rests on distinguishing the variety of solutions satisfying the limit condition at infinity. To solve an auxiliary Cauchy problem, we apply expansions of a solution in the parameter.

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References

  1. Voevodin V. V. and Kuznetsov Yu. A., Matrices and Calculations [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  2. Konyukhova N. B. and Pak T. V., “Transfer of admissible boundary conditions at infinity for systems of linear ordinary differential equations with a large parameter,” Zh. Vychisl. Mat. i Mat. Fiz., 27, No. 6, 847-866 (1987).

    Google Scholar 

  3. Abramov A. A., Balla K., and Konyukhova N. B., “Transfer of boundary conditions from singular points for systems of ordinary differential equations,” in: Soobshch. po Vychisl. Matematike, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1981.

  4. Konyukhova N. B., “Smooth Lyapunov manifolds and singular boundary problems,” in: Soobshch. po Vychisl. Matematike, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1996.

  5. Zadorin A. I., “Numerical solution of an equation with a small parameter on an infinite interval,” Zh. Vychisl. Mat. i Mat. Fiz., 38, No. 10, 1671-1682 (1998).

    Google Scholar 

  6. Zadorin A. I., “Transferring a boundary condition from infinity in the case of numeric solution to second-order linear equations with a small parameter,” Sibirsk. Zh. Vychisl. Mat., 2, No. 1, 21-35 (1999).

    Google Scholar 

  7. Konyukhova N. B. and Pak T. V., “Singular Cauchy problems with a large parameter for systems of nonlinear ordinary differential equations,” Zh. Vychisl. Mat. i Mat. Fiz., 27, No. 4, 501-519 (1987).

    Google Scholar 

  8. Konyukhova N. B., “A stationary Lyapunov problem for a system of first-order quasilinear partial differential equations,” Differentsial'nye Uravneniya, 30, No. 8, 1384-1395 (1994).

    Google Scholar 

  9. Coddington E. A. and Levinson N., Theory of Ordinary Differential Equations [Russian translation], Izdat. Inostr. Lit., Moscow (1958).

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  1. The Institute of Applied Mathematics of the Far East Division of the, Russian Academy of Sciences, Khabarovsk

    A. I. Zadorin

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  1. A. I. Zadorin
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Zadorin, A.I. Reduction from a Semi-Infinite Interval to a Finite Interval of a Nonlinear Boundary Value Problem for a System of Second-Order Equations with a Small Parameter. Siberian Mathematical Journal 42, 884–892 (2001). https://doi.org/10.1023/A:1011959409568

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  • DOI: https://doi.org/10.1023/A:1011959409568

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