dc.contributor.author Denche, Mohamed ( ) dc.contributor.author Guerfi, Amara ( ) dc.date.accessioned 2021-08-02T20:47:07Z dc.date.available 2021-08-02T20:47:07Z dc.date.issued 2007-01-08 dc.identifier.citation Denche, M., & Guerfi, A. (2007). Boundary-value problems for ordinary differential equations with matrix coefficients containing a spectral parameter. Electronic Journal of Differential Equations, 2007(14), pp. 1-9. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/14164 dc.description.abstract In the present work, we study a multi-point boundary-value problem for an ordinary differential equation with matrix coefficients containing a spectral parameter in the boundary conditions. Assuming some regularity conditions, we show that the characteristic determinant has an infinite number of zeros, and specify their asymptotic behavior. Using the asymptotic behavior of Green matrix on contours expending at infinity, we establish the series expansion formula of sufficiently smooth functions in terms of residuals solutions to the given problem. This formula actually gives the completeness of root functions as well as the possibility of calculating the coefficients of the series. en_US dc.format Text dc.format.extent 9 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Characteristic determinant en_US dc.subject Expansion formula en_US dc.subject Green matrix en_US dc.subject Regularity conditions en_US dc.title Boundary-value problems for ordinary differential equations with matrix coefficients containing a spectral parameter en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
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