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

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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 the 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 the 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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Authors and Affiliations

  1. Institute of Mathematics of the Ministry of Education and Science and National Academy of Sciences of the Republic of Kazakhstan, Kazakhstan

    A. T. Asanova

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  1. A. T. Asanova
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Correspondence to A. T. Asanova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 21–39, 2006.

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Asanova, A.T. On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations. J Math Sci 150, 2302–2316 (2008). https://doi.org/10.1007/s10958-008-0130-0

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  • DOI: https://doi.org/10.1007/s10958-008-0130-0

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