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Smooth Solution of an Initial Value Problem for a Mixed-Type Differential Difference Equation

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

In this paper, we show the construction of the solution to the mixed type differential difference equation:

$$\begin{aligned} x'(t)= A x(t+ a)+ Bx(t-a)+Cx(t), \end{aligned}$$

where \(A,B,C\in\mathbb{C}\setminus\{0\}\), a>0 and \(t \in\mathbb{R}\). We use a step derivative method and a certain condition on the initial function φ∈C ∞[−a,a] to assure the existence, uniqueness and smoothness of the solution in \(\mathbb{R}\).

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Authors and Affiliations

  1. Departamento de Matemáticas Puras y Aplicadas, Universidad Simón Bolívar, P.O. Box 89000, 1080, Caracas, Venezuela

    Valentina Iakovleva & Judith Vanegas

Authors
  1. Valentina Iakovleva
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  2. Judith Vanegas
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Corresponding author

Correspondence to Valentina Iakovleva .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Iakovleva, V., Vanegas, J. (2015). Smooth Solution of an Initial Value Problem for a Mixed-Type Differential Difference Equation. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_70

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