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An Issue About the Existence of Solutions for a Linear Non-autonomous MTFDE

  • M. Filomena TeodoroEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 164)

Abstract

This article is concerned with the existence of solution of a certain non-autonomous linear delayed-advanced differential equation. The main objective is to provide the proof of a theorem introduced in Lima et al. (J. Comput. Appl. Math. 234(9):2732–2744, 2010) about existence of solution of a class of mixed-type functional differential equations (MTFDEs). It is an effort to complete the theoretical basis of some computational methods introduced earlier to solve numerically such equations, which were deduced making use of that theorem.

Keywords

Mixed-type functional differential equation Method of steps Boundary value problem Existence of solution 

Mathematics Subject Classification (2000):

PACS: 02.30 Ks 02.60 Lj 2000 MSC: 34K06 34K28 65Q05 34K10 

Notes

Acknowledgements

This work was supported by Portuguese funds through the Center for Computational and Stochastic Mathematics (CEMAT), The Portuguese Foundation for Science and Technology (FCT), University of Lisbon, Portugal, project UID/Multi/04621/2013, and Center of Naval Research (CINAV), Naval Academy, Portuguese Navy, Portugal.

The author also acknowledges Professors P. Lima, N. Ford, and P. Lumb for maintaining their availability and the provided suggestions.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.CEMAT, Instituto Superior TécnicoLisbon UniversityLisboaPortugal
  2. 2.CINAV, Naval AcademyBase Naval de LisboaAlmadaPortugal

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