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Multiple Solutions in Systems of Functional Differential Equations

  • Hippolyte D'Albis


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Emmanuelle Augeraud-Véron


    (MIA - Mathématiques, Image et Applications - Université de La Rochelle)

  • Hermen Jan Hupkes


    (University of Missouri - Columbia - Mathematics Department)

This paper proposes conditions for the existence and uniqueness of solutions to systems of linear differential or algebraic equations with delays or advances, in which some variables may be non predetermined. The obtained conditions represent the counterpart of the Blanchard and Kahn conditions for the considered functional equations.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00786419.

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Date of creation: Jan 2013
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Handle: RePEc:hal:cesptp:halshs-00786419
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  1. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
  2. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Functional Differential-Algebraic Equations of Mixed Type," Documents de travail du Centre d'Economie de la Sorbonne 12043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, vol. 52(3), pages 665-80, May.
  5. Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
  6. BOUCEKKINE, RAOUF & de la CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs : principles and applications," CORE Discussion Papers 2004047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
  8. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 227-236.
  9. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Documents de travail du Centre d'Economie de la Sorbonne 12026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  10. Mauro Bambi and Omar Licandro, 2015. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  11. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  12. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
  13. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 1-15, February.
  14. Bambi, Mauro & Fabbri, Giorgio & Gozzi, Fausto, 2009. "Optimal policy and consumption smoothing effects in the time-to-build AK model," MPRA Paper 17128, University Library of Munich, Germany.
  15. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-46, November.
  16. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
  17. Gray, Malcolm R & Turnovsky, Stephen J, 1979. "Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models," Econometrica, Econometric Society, vol. 47(6), pages 1457-74, November.
  18. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  19. repec:fda:fdaddt:2004-07 is not listed on IDEAS
  20. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
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