Strong solutions of a neutral type equation with finite delay

  • Verónica Poblete
  • Felipe Poblete
  • Juan C. PozoEmail author


This paper is concerned to study the existence and uniqueness of solution of neutral type differential equations, by using the maximal regularity property of the first-order abstract Cauchy problem with finite delay on Lebesgue spaces defined at the line. The main tools that we use to achieve our goals are an operator-valued version of Miklhin’s Fourier multiplier theorem, weighted Sobolev spaces on the real line and fixed point arguments.

Mathematics Subject Classification

Primary 34K40 Secondary 34G10 42B15 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Verónica Poblete
    • 1
  • Felipe Poblete
    • 2
  • Juan C. Pozo
    • 3
    Email author
  1. 1.Departamento de Matemáticas, Facultad de CienciasUniversidad de ChileSantiagoChile
  2. 2.Instituto de Ciencias Físicas y Matemáticas, Facultad de CienciasUniversidad Austral de ChileValdiviaChile
  3. 3.Departamento de Matemáticas y EstadísticasFacultad de Ingeniería y CienciasTemucoChile

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