Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations

Abstract

The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators L p-multipliers and UMD-spaces.

Existence and Uniqueness Fourth-order Differential Equations in Banach Space Having Fourier Type

“…In particular, the problem of existence of periodic solutions, has been considered by several authors. We refer the readers to papers [ [1], [5], [7], [14]] and the references listed therein for information on this subject. In this work, we study the existence of periodic solutions for the following integro-differential equations with delay In [7], Bahloul et al established the existence of a periodic solution for the following partial functional differential equation.…”

R-boundedness Approach to linear third differential equations in a UMD Space

“…Bátkai et al [5] obtained results on the hyperbolicity of delay equations using the theory of operatorvalued Fourier multipliers. Bu [8] has studied C α -maximal regularity for the problem (1.2) on R. Recently, Lizama [14] obtained necessary and sufficient conditions for the first order delay equation (1.2) to have L p -maximal regularity using multiplier theorems on L p -(T;X), and C α -maximal regularity of the corresponding equation on the real line has been studied by Lizama and Poblete [15].…”