Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/16206
Title: On general properties of n-th order retarded functional differential equations
Authors: Benevieri, Pierluigi
Calamai, Alessandro
Furi, Massimo
Pera, Maria Patrizia
Keywords: Retarded functional differential equations (RFDEs)RFDEs with infinite delayinitial value problemsproperties of solutions
Issue Date: 2017
Source: P. Benevieri, A. Calamai et al., "On general properties of n-th order retarded functional differential equations", in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics", 49 (2017), Trieste, EUT Edizioni Università di Trieste, 2017, pp. 73-93
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Part of: 49 (2017)
Abstract: Consider the second order RFDE (retarded functional differential equation) x’’ (t) = f(t, xt), where f is a continuous realvalued function defined on the Banach space R x C1([−r, 0],R). The weak assumption of continuity on f (due to the strong topology of C1([−r, 0],R)) makes not convenient to transform this equation into a first order RFDE of the type z’ (t) = g(t, zt). In fact, in this case, the associated R2-valued function g could be discontinuous (with the C0- topology) and, in addition, not necessarily defined on the whole space R x C([−r, 0],R2). Consequently, in spite of what happens for ODEs, the classical results regarding existence, uniqueness, and continuous dependence on data for first order RFDEs could not apply. Motivated by this obstruction, we provide results regarding general properties, such as existence, uniqueness, continuous dependence on data and continuation of solutions of RFDEs of the type x(n)(t) = f(t, xt), where f is an Rk-valued continuous function on the Banach space R x C(n−1)([−r, 0],Rk). Actually, for the sake of generality, our investigation will be carried out in the case of infinite delay.
URI: http://hdl.handle.net/10077/16206
ISSN: 0049-4704
eISSN: 2464-8728
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017)

Files in This Item:
File Description SizeFormat 
06_RIMUT_BenevierietAl.pdf338.49 kBAdobe PDFView/Open
Show full item record


CORE Recommender

Page view(s)

24
checked on Jun 20, 2018

Download(s)

9
checked on Jun 20, 2018

Google ScholarTM

Check


This item is licensed under a Creative Commons License Creative Commons