Boundary-value problems for ordinary differential equations with matrix coefficients containing a spectral parameter
Date
2007-01-08
Authors
Denche, Mohamed
Guerfi, Amara
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Characteristic determinant, Expansion formula, Green matrix, Regularity conditions
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.
Rights
Attribution 4.0 International