Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints

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• 作者：Luca Bisconti (1)
  Alessandro Calamai (2)
  Marco Spadini (1)
  
  1. Dipartimento di Matematica e Informatica ; Universit脿 di Firenze ; Via S. Marta 3 ; Firenze ; 50139 ; Italy
  2. Dipartimento di Ingegneria Industriale e Scienze Matematiche ; Universit脿 Politecnica delle Marche ; Via Brecce Bianche ; Ancona ; 60131 ; Italy
  
• 关键词：34A09 ; 34C25 ; 34C40 ; differential ; algebraic equations ; periodic solutions ; ordinary differential equations on manifolds
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,217 KB
• 参考文献：1. Kunkel, P, Mehrmann, V (2006) Differential-Algebraic Equations: Analysis and Numerical Solution. CrossRef
  2. Rabier, PJ, Rheinbolt, WC Theoretical and numerical analysis of differential-algebraic equations. In: Ciarlet, PG, Lions, JL eds. (2002) Handbook of Numerical Analysis. Elsevier, Amsterdam, pp. 183-540
  3. Rheinboldt, WC (1984) Differential-algebraic systems as differential equations on manifolds. Math. Comput. 43: pp. 473-482 CrossRef
  4. Bisconti, L (2012) Harmonic solutions to a class of differential-algebraic equations with separated variables. Electron. J. Differ. Equ. 2012: CrossRef
  5. Bisconti, L, Spadini, M: Harmonic perturbations with delay of periodic separated variables differential equations. Topol. Methods Nonlinear Anal. (to appear)
  6. Calamai, A (2011) Branches of harmonic solutions for a class of periodic differential-algebraic equations. Commun. Appl. Anal. 15: pp. 273-282
  7. Calamai, A, Spadini, M (2012) Branches of forced oscillations for a class of constrained ODEs: a topological approach. Nonlinear Differ. Equ. Appl. 19: pp. 383-399 CrossRef
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  9. Spadini, M (2010) A note on topological methods for a class of differential-algebraic equations. Nonlinear Anal. 73: pp. 1065-1076 CrossRef
  10. Furi, M, Pera, MP, Spadini, M The fixed point index of the Poincar茅 operator on differentiable manifolds. In: Brown, RF, Furi, M, G贸rniewicz, L, Jiang, B eds. (2005) Handbook of Topological Fixed Point Theory. Spinger, Dordrecht
  11. Milnor, JW (1965) Topology from the Differentiable Viewpoint. University Press of Virginia, Charlottesville
  12. Benevieri, P, Furi, M, Pera, MP, Spadini, M: An Introduction to topological degree in euclidean spaces. Technical Report N. 42, Gennaio 2003, Universit脿 di Firenze, Dipartimento di Matematica Applicata, (2003)
  13. Gerdin, M: Identification and estimation for models described by differential-algebraic equations. Department of Electrical Engineering Link枚pings universitet, SE-581 83 (2006)
  14. Bisconti, L, Spadini, M (2011) On a class of differential-algebraic equations with infinite delay. Electron. J. Qual. Theory Differ. Equ. 2011:
  15. Bisconti, L, Spadini, M (2012) Corrigendum to On a class of differential-algebraic equations with infinite delay. Electron. J. Qual. Theory Differ. Equ. 2012: CrossRef
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized differential-algebraic equations with non-autonomous constraints of a particular type. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions of the considered equations. Our approach is based on topological arguments as regards differential equations on implicitly defined manifolds, combined with elementary facts of matrix analysis.