Existence and asymptotic stability of periodic solutions for neutral evolution equations with delay

Qiang Li; Mei Wei

doi:10.3934/eect.2020032

Article Contents

2020, Volume 9, Issue 3: 753-772. Doi: 10.3934/eect.2020032

This issue Previous Article Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data Next Article Continuity with respect to fractional order of the time fractional diffusion-wave equation

Existence and asymptotic stability of periodic solutions for neutral evolution equations with delay

Qiang Li^, and
Mei Wei^,

Department of Mathematics, Shanxi Normal University, Linfen 041000, China

^* Corresponding author. Qiang Li and Mei Wei
^* Corresponding author. Qiang Li and Mei Wei

Received: July 2019

Revised: October 2019

Early access: December 2019

Published: September 2020

Research supported by NNSF of China (11261053) and NSF of Gansu Province (1208RJZA129)

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Abstract

In this paper, we are devoted to consider the periodic problem for the neutral evolution equation with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of periodic mild solutions for the equation. In addition, with the aid of a new integral inequality with delay, we present essential conditions on the nonlinear function to guarantee that the equation has an asymptotically stable periodic mild solution.

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Mathematics Subject Classification: 34K30, 47H07, 47H08.

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