On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations |
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Authors: | A T Asanova |
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Institution: | (1) Institute of Mathematics of the Ministry of Education and Science and National Academy of Sciences of the Republic of Kazakhstan, Kazakhstan |
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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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 21–39, 2006. |
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