EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR PARABOLIC EQUATION WITH NONLOCAL DELAY

被引：9

作者：

Li, Qiang ^{[1
]}

Li, Yongxiang ^{[1
]}

Chen, Pengyu ^{[1
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

KODAI MATHEMATICAL JOURNAL | 2016年 / 39卷 / 02期

关键词：

Parabolic equation with nonlocal delay; Time periodic mild solutions; Existence and uniqueness; Semigroup of Operator; Lower and upper solutions; Monotone iterative technique; EVOLUTION-EQUATIONS; WAVE-FRONTS; DIFFERENTIAL-EQUATIONS; ASYMPTOTIC STABILITY; DIFFUSION-EQUATIONS; BOUNDARY-CONDITIONS; POPULATION-MODEL; TRAVELING-WAVES; TIME DELAYS; SYSTEMS;

D O I：

10.2996/kmj/1467830137

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the existence and uniqueness of time periodic solutions for the general periodic parabolic equation boundary problem with nonlocal delay. We apply operator semigroup theory and monotone iterative technique of lower and upper solutions to obtain the existence and uniqueness of omega-periodic mild solutions of some abstract evolution equation under some quasimonotone conditions. In the end, applying our abstract results to parabolic equation with nonlocal delay, we get the existence and uniqueness of omega-periodic solution, which generalize the recent conclusions on this issue.

引用

页码：276 / 289

页数：14

共 50 条

[41] On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay
Wang Lian
Wang Muqiu
Li Liming Institute of Mathematics Academia Sinica Beijing
Acta Mathematica Sinica,English Series, 1994, (01) : 88 - 98
[42] The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay
Zhang, Xianmin
Huang, Xiyue
Liu, Zuohua
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (04) : 775 - 781
[43] The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems
Liu, Bingwen
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (06) : 3145 - 3151
[44] On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay
Wang Lian
Wang Muqiu
Li Liming Institute of Mathematics Academia Sinica Beijing China Hebei Institute of Finance and Economics Shijiazhuang China
Acta Mathematica Sinica(New Series), 1994, 10 (01) : 88 - 98
[45] Existence, uniqueness and regularity for nonlinear parabolic equations with nonlocal terms
Alibaud, Nathael
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 14 (3-4): : 259 - 289
[46] Existence, uniqueness and regularity for nonlinear parabolic equations with nonlocal terms
Nathaël Alibaud
Nonlinear Differential Equations and Applications NoDEA, 2007, 14 : 259 - 289
[47] Global existence of solutions of initial boundary value problem for nonlocal parabolic equation with nonlocal boundary condition
Gladkov, Alexander
Kavitova, Tatiana
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (08) : 5464 - 5479
[48] Existence and uniqueness results for a class of nonlocal elliptic and parabolic problems
Chipot, M
Lovat, B
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS, 2001, 8 (01): : 35 - 51
[49] Existence, Uniqueness and Stability of Mild Solutions to a Stochastic Nonlocal Delayed Reaction–Diffusion Equation
Wenjie Hu
Quanxin Zhu
Neural Processing Letters, 2021, 53 : 3375 - 3394
[50] On the existence and uniqueness of time periodic solutions for a semilinear heat equation in the whole space
Deng, Jian
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (03) : 796 - 802

← 1 2 3 4 5 →