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 Fundam. Prikl. Mat., 2006, Volume 12, Issue 4, Pages 21–39 (Mi fpm957)

On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations

A. T. Asanova

Institute of Mathematics, Ministry of Education and Science of the Republic of Kazakhstan

Abstract: We consider a family of two-point boundary-value problems for systems of ordinary differential equations with functional parameters. This family is the result of the reduction of a boundary-value problem with nonlocal condition for a system of second-order quasilinear hyperbolic equations by introduction of additional functions. Using the parametrization method, we establish necessary and sufficient conditions of the unique solvability of the family of two-point boundary-value problems for a linear system in terms of initial data. We also prove sufficient conditions of the unique solvability of the problem considered and propose an algorithm for its solution.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:5, 2302–2316

Bibliographic databases:

UDC: 517.925+517.95

Citation: A. T. Asanova, “On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations”, Fundam. Prikl. Mat., 12:4 (2006), 21–39; J. Math. Sci., 150:5 (2008), 2302–2316

Citation in format AMSBIB
\Bibitem{Ass06} \by A.~T.~Asanova \paper On the unique solvability of a~family of two-point boundary-value problems for systems of ordinary differential equations \jour Fundam. Prikl. Mat. \yr 2006 \vol 12 \issue 4 \pages 21--39 \mathnet{http://mi.mathnet.ru/fpm957} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314143} \zmath{https://zbmath.org/?q=an:1151.35402} \transl \jour J. Math. Sci. \yr 2008 \vol 150 \issue 5 \pages 2302--2316 \crossref{https://doi.org/10.1007/s10958-008-0130-0} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42149195075} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. T. Assanova, A. E. Imanchiev, “On conditions of the solvability of nonlocal multi-point boundary value problems for quasi-linear systems of hyperbolic equations”, Eurasian Math. J., 6:4 (2015), 19–28
2. Asanova A.T., “on Solvability of Nonlinear Boundary Value Problems With Integral Condition For the System of Hyperbolic Equations”, Electron. J. Qual. Theory Differ., 2015, no. 63, UNSP 63
3. A. T. Assanova, A. P. Sabalakhova, “On the unique solvability of nonlocal problems with integral conditions for a hybrid system of partial differential equations”, Eurasian Math. J., 9:3 (2018), 14–24
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