Geodesic
On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 21-39 
A. T. Asanova. On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 21-39. http://geodesic.mathdoc.fr/item/FPM_2006_12_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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