Abstract
As we already noted at the beginning of Chap. 2, the need of introducing delays in the description of natural phenomena was clearly stated early in the past century and a first important contribution was due to Vito Volterra in the field of the class of equations that, after him, are actually named Volterra Equations (see 7 and the brief historical review in 1). However, delay equations, in the case of concentrated delays as well as of distributed delays, in their classical form or in the abstract context of Functional Differential Equations, have an extensive development starting with the 1950's. This appendix is mainly designed to meet the needs arising in the context of the basic models discussed in Chap. 2 and provides a minimal pathway through the subject. The reader may refer to 2, 3, 6 for a full treatment.
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References
Arino, O., Hbid, M.L. , Ait Dads, E. (Eds.): Delay Differential Equations and Applications. Springer, Netherlands (2006)
Bellman, R., Cooke, K.L.: Differential-Difference Equations. Academic Press, New York (1963)
Diekmann, O., van Gils, S.A., Lunel, S., Walther, H.O.: Delay Equations: Functional, Complex, and Nonlinear Analysis. Applied Mathematical Science 110, Springer, New York (1991)
Doetsch, G.: Introduction to the Theory and Application of the Laplace Transformation. Springer-Verlag, Berlin Heidelberg (1974)
Hale, J.K., Lunel, S.: Introduction to Functional Differential Equations. Applied Mathematical Science 99, Springer, New York (1993)
Gripenberg, G. , Londen, S-O., Staffans, O.: Volterra Integral and Functional Equations. Cambridge University Press, Cambridge (1990)
Volterra, V.: Lecons sur les Équations Intégrales et les Équations intégro-différentielles. Gauthier-Villars, Paris (1913)
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Iannelli, M., Pugliese, A. (2014). Delay Equations. In: An Introduction to Mathematical Population Dynamics. UNITEXT(), vol 79. Springer, Cham. https://doi.org/10.1007/978-3-319-03026-5_Appendix-B
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DOI: https://doi.org/10.1007/978-3-319-03026-5_Appendix-B
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