On the Kiguradze theorem for linear boundary-value problems
DOI:
https://doi.org/10.15407/dopovidi2017.12.008Keywords:
linear boundary-value problem, passage to the limit, system of ordinary differential equationsAbstract
We investigate the limiting behavior of solutions of inhomogeneous boundary-value problems for the systems of linear ordinary differential equations on a finite interval. A generalization of the Kiguradze theorem (1987) on the passage to the limit is obtained.
Downloads
References
Reid, W. T. (1967). Some limit theorems for ordinary differential systems. J. Diff. Equat. 3, No. 3, pp. 423-439. doi: https://doi.org/10.1016/0022-0396(67)90042-3
Opial, Z. (1967). Continuous parameter dependence in linear systems of differential equations. J. Diff. Equat. 3, pp. 571-579. doi: https://doi.org/10.1016/0022-0396(67)90017-4
Levin, A. Yu. (1967). Passage to the limit for nonsingular systems X⋅ = An(t)X. Sov. Math. Dokl. 176, No. 4, pp. 774-777.
Levin, A. Yu. (1973). Problems of the theory of ordinary differential equations. I. Vestn. Yaroslav. Univ. Iss. 5, pp. 105-132 (Russian).
Nguyen, Tkhe Hoan. (1993). Dependence of the solutions of a linear system of differential equations on a parameter. Differential Equations. 29, No. 6, pp. 830-835.
Kiguradze, I. T. (1975). Some singular boundary value problems for ordinary differential equations. Tbilisi: Izdat. Tbilis. Univ. (Russian).
Kiguradze, I. T. (1988). Boundary-value problems for systems of ordinary differential equations. J. Soviet Math. 43, No. 2, pp. 2259-2339. doi: https://doi.org/10.1007/BF01100360
Kodliuk, T. I., Mikhailets, V. A. & Reva, N. V. (2013). Limit theorems for one-dimensional boundary-value problems. Ukr. Math. J. 65, No. 1, pp. 77-90. doi: https://doi.org/10.1007/s11253-013-0766-x
Gnyp, E. V., Kodliuk, T. I. & Mikhailets, V. A. (2015). Fredholm boundary-value problems with parameter in Sobolev spaces. Ukr. Math. J. 67, No. 5, pp. 658-667. doi: https://doi.org/10.1007/s11253-015-1105-1
Mikhailets, V. A., Murach, A. A. & Soldatov, V. A. (2016). Continuity in a parameter of solutions to generic boun dary-value problems. Electron. J. Qual. Theory Differ. Equat. No. 87, pp. 1-16. doi: https://doi.org/10.14232/ejqtde.2016.1.87
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
