On a class of differential-algebraic equations with infinite delay
Copyright policy )On a class of differential-algebraic equations with infinite delay
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.
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 5.7
QA Mathematics / matematika, periodic solution, Dynamical Systems (math.DS), periodic perturbation, differential-algebraic equations, Mathematics - Classical Analysis and ODEs, infinite delay, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, retarded functional equations, Mathematics - Dynamical Systems, 34A09, 34K13, 34C40, differential-algebraic equations; Retarded functional differential equations; degree of a tangent vector field, Mathematics
QA Mathematics / matematika, periodic solution, Dynamical Systems (math.DS), periodic perturbation, differential-algebraic equations, Mathematics - Classical Analysis and ODEs, infinite delay, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, retarded functional equations, Mathematics - Dynamical Systems, 34A09, 34K13, 34C40, differential-algebraic equations; Retarded functional differential equations; degree of a tangent vector field, Mathematics
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