Abstract
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.
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Juan C. Pozo: Partially supported by FONDECYT Grant 11160295. Felipe Poblete: Partially supported by FONDECYT Grant 11181263. Verónica Poblete: Partially supported by Enlace ENL016/15 y PAIFAC.
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Poblete, V., Poblete, F. & Pozo, J.C. Strong solutions of a neutral type equation with finite delay. J. Evol. Equ. 19, 361–386 (2019). https://doi.org/10.1007/s00028-019-00478-9
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DOI: https://doi.org/10.1007/s00028-019-00478-9