Contemporary theory of FDEs and some classical problems
by
N.V. Azbelev
Perm State Technical University
Coauthors: P.M. Simonov

A study of Functional Differential Equations (FDEs) in Banach spaces is presented leading to the general notion of Abstract FDEs and to new consideration of many classical problems. This includes a new approach to stability and asymptotic behavior of solutions, the regularization of singular problems by their transformation to properly chosen functional spaces, and an extension of the calculus of variations based on the use of the original W-transformation

References

1. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F., The elements of the contemporary theory of functional differential equations. Methods and applications, Institute of computer assisted research, Moscow (2002).

2. Azbelev N.V., Simonov P.M., Stability of differential equations with aftereffect, Taylor and Francis, London and New York (2002).

The research was supported by the RFBR (03-01-00255, 04-01-96016), and by the Program Üniversity of Russia" (ur.03.01.020), and by the Competitive Center of Fundamental Natural Science (E02-2.0-63), and by the Company "Prognoz".

Date received: March 25, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canu-82.