EXISTENCE AND ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR NEUTRAL EVOLUTION EQUATIONS WITH DELAY

被引：12

作者：

Li, Qiang ^{[1
]}

Wei, Mei ^{[1
]}

机构：

[1] Shanxi Normal Univ, Dept Math, Linfen 041000, Shanxi, Peoples R China

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2020年 / 9卷 / 03期

关键词：

Neutral evolution equation; periodic mild solutions; compact analytic semigroup; existence and uniqueness; asymptotic stability; FUNCTIONAL-DIFFERENTIAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; ALPHA-NORM;

D O I：

10.3934/eect.2020032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：753 / 772

页数：20

共 50 条

[41] Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force
Kozono, Hideo
Mashiko, Yuki
Takada, Ryo
JOURNAL OF EVOLUTION EQUATIONS, 2014, 14 (03) : 565 - 601
[42] Existence theorems and periodic solutions of neutral integral equations
Burton, TA
Furumochi, T
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 43 (04) : 527 - 546
[43] Existence and Asymptotic Stability of Periodic Solutions of the Reaction–Diffusion Equations in the Case of a Rapid Reaction
N. N. Nefedov
E. I. Nikulin
Russian Journal of Mathematical Physics, 2018, 25 : 88 - 101
[44] Existence of periodic solutions of second order neutral equations
Feng, Zhaosheng
Beijing Hangkong Hangtian Daxue Xuebao/Journal of Beijing University of Aeronautics and Astronautics, 1995, 21 (02): : 114 - 118
[45] Asymptotic Stability of Solutions to Delay Difference Equations
Demidenko G.V.
Baldanov D.S.
Journal of Mathematical Sciences, 2017, 221 (6) : 815 - 825
[46] Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations
Yu, Zhanhua
Liu, Mingzhu
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2011, 2011
[47] Asymptotic stability of solutions delay differential equations
Peng, YH
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2006, 13 : 859 - 866
[48] EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR EQUATIONS OF EVOLUTION
BROWDER, FE
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 53 (05) : 1100 - &
[49] Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay
Ren, Yong
Xia, Ningmao
APPLIED MATHEMATICS AND COMPUTATION, 2009, 210 (01) : 72 - 79
[50] Existence of ahnost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay
Ma, Xiao
Shu, Xiao-Bao
Mao, Jianzhong
STOCHASTICS AND DYNAMICS, 2020, 20 (01)

← 1 2 3 4 5 →