Some functional differential equations with both retarded and advanced arguments

Authors

  • Veronica Ana Ilea Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat381-900

Keywords:

functional-differential equations, boundary value problems, contraction's principle, Schauder's fixed point principle
Abstract views: 200

Abstract

In this paper we shall study a functional differential equation of mixed type. This equation is a generalization of some equations from medicine. Related to this equation we study the existence of the solution by contraction's principle and Schauder's fixed point theorem.

Downloads

Download data is not yet available.

References

Aronson, D.G. and Weinberger, H.F., Nonlinear diffusion in population genetics, combustion and nerve propagation, "Lectures Notes in Mathematics", 446, Springer-Verlag, Berlin, pp. 5-49, 1975, https://doi.org/10.1007/bfb0070595 DOI: https://doi.org/10.1007/BFb0070595

Mallet-Paret, J., The global structure of traveling waves in spatially discrete dynamical systems, J. Dyn. Diff Eq., 11, no. 1, pp. 49-127, 1999, https://doi.org/10.1023/a:1021841618074 DOI: https://doi.org/10.1023/A:1021841618074

Mallet-Paret, J., The Freedholm alternative for functional differential equations of mixed type, J. Dyn. Diff Eq., 11, no. 1, pp. 1-46, 1999, https://doi.org/10.1023/a:1021889401235 DOI: https://doi.org/10.1023/A:1021889401235

Mallet-Paret, J. and Lunel, S.V., Exponential dichotomies and Wiener-Hopf factorizations for mixed-type functional differential equations, 2001, www.dam.brown.edu/lcds/publications.textonly.html.

Precup, R., Some existence results for differential equations with both retarded and advanced arguments, Mathematica, 44 (67), no. 1, pp. 31-38, 2002.

Rus, I.A. and Dârzu-Ilea, V.A., First order functional-differential equations with both advanced and retarded arguments, Fixed Point Theory, 5, no. 1, pp. 103-115, 2004.

Rustichini, A., Functional differential equation of mixed type: The linear autonomous case, J. Dyn. Diff. Eq., 1, pp. 121-143, 1989, https://doi.org/10.1007/bf01047828 DOI: https://doi.org/10.1007/BF01047828

Rustichini, A., Hopf bifurcation for functional differential equation of mixed type, J. Dyn. Diff. Eq., 1, pp. 145-177, 1989, https://doi.org/10.1007/bf01047829 DOI: https://doi.org/10.1007/BF01047829

Schulman, L.S., Some differential difference equations containing both advance and retardation, J. Math. Phys., 15, pp. 195-198, 1974. DOI: https://doi.org/10.1063/1.1666641

Wu, J. and Zou, X., Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Diff. Eq., 135, pp. 315-357, 1997, https://doi.org/10.1006/jdeq.1996.3232 DOI: https://doi.org/10.1006/jdeq.1996.3232

Downloads

Published

2009-02-01

How to Cite

Ilea, V. A. (2009). Some functional differential equations with both retarded and advanced arguments. Rev. Anal. Numér. Théor. Approx., 38(1), 41–49. https://doi.org/10.33993/jnaat381-900

Issue

Vol. 38 No. 1 (2009)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.