Mohamed Denche, Amara Guerfi
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.
Show me the PDF file (239K), TEX file, and other files for this article.
 |
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 |
Return to the EJDE web page