Topological Methods in Nonlinear Analysis

A nonstandard description of retarded functional differential equations

Thomas Elsken

Full-text: Open access


We develop a nonstandard description of Retarded Functional Differential Equations which consist of a formally finite iteration of vectors. We present two applications where the new description gives explicit formulae. The classical approach in these cases only offers a method to construct the solution.

Article information

Topol. Methods Nonlinear Anal., Volume 19, Number 1 (2002), 153-198.

First available in Project Euclid: 2 August 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Elsken, Thomas. A nonstandard description of retarded functional differential equations. Topol. Methods Nonlinear Anal. 19 (2002), no. 1, 153--198.

Export citation


  • I. Ben El Mamoune, E. Benoit and C. Lobry, Une Version Non Standard du Théorème de F. Riesz, C. R. Acad. Sci. Paris Sér. I, 316 , 653–656 (1993) \ref
  • E. Benoit, Dynamical bifurcations , Proc. Luminy, France (1990);, Lecture Notes Mathematics, 1493 (1991) \ref
  • C. W. Cryer, Numerical methods for functional differential equations , Delay and Functional Differential Equations and their Applications, Academic Press, New York (1972 (K. Schmitt, ed.)) \ref
  • P. Delfini and C. Lobry, The vibrating string (F. Diener, M. Diener, Nonstandard Analysis in Practice, eds.), Springer, Berlin (1995) \ref
  • M. Diener and G. Wallet, Mathematique Finitaires and Analyse Non Standard, t. 1, 2, Publications Mathematiques de l'Universite Paris VII, 31 , Paris (1989) \ref
  • J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, App. Math. Sci., 99 , Springer–Verlag, New York (1993) \ref
  • A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Analysis, Academic Press, Orlando, Fl. (1985) \ref
  • D. Landers and L. Rogge, Nichtstandard Analysis, Springer– Verlag, Berlin (1994) \ref
  • L. Pandolfi, On feedback stabilization of functional differential equations , Boll. Un. Mat. Ital., 11 (1975), 626–635