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On a class of differential-algebraic equations with infinite delay

By Luca Bisconti and Marco Spadini

Abstract

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations.Comment: 13 pages. Revision: Incorporate changes suggested by readers. Corrected a few typos across the paper, definition of BU added, revised the (previously incorrect) definition of solution of RFDAE, made slight changes in the Introduction. Replacement of Dec. 6, 2012: introduced further changes suggested by referee, bundled addendum/erratum containing a corrected version of Lemma 5.5 and Corollary 5.

Topics: Mathematics - Classical Analysis and ODEs, Mathematics - Dynamical Systems, 34A09, 34K13, 34C40
Year: 2012
OAI identifier: oai:arXiv.org:1104.0141
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