Electron. J. Diff. Eqns., Vol. 2007(2007), No. 14, pp. 1-9.

Boundary-value problems for ordinary differential equations with matrix coefficients containing a spectral parameter

Mohamed Denche, Amara Guerfi

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.

Submitted August 15, 2006. Published January 8, 2007.
Math Subject Classifications: 34L10, 34E05, 47E05.
Key Words: Characteristic determinant; expansion formula; Green matrix; regularity conditions.

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Mohamed Denche
Laboratoire Equations Differentielles
Departement de Mathematiques, Faculté des Sciences
Université Mentouri, Constantine, 25000 Constantine, Algeria
email: denech@wissal.dz
Amara Guerfi
Department of Mathematics and Computer engineering
Faculty of Science and Engineering
University of Ouargla, 30000 Ouargla, Algeria
email: amaraguerfi@yahoo.fr

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