Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 14, pp. 1-9.
Title: Boundary-value problems for ordinary differential equations with
matrix coefficients containing a spectral parameter
Authors: Mohamed Denche (Univ. Mentouri, Constantine, Algeria)
Amara Guerfi (Univ. of Ouargla, Algeria)
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.
Submitted August 15, 2006. Published January 8, 2007.
Math Subject Classifications: 34L10, 34E05, 47E05.
Key Words: Characteristic determinant; expansion formula;
Green matrix; regularity conditions.