American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index
  • CPAA Home
  • This Issue
  • Next Article
    Effects of small viscosity and far field boundary conditions for hyperbolic systems
June  2004, 3(2): 291-300. doi: 10.3934/cpaa.2004.3.291

On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations

Nguyen Minh Man 1, and  Nguyen Van Minh 2,

1. 

Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam
2. 

Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam

Received  January 2003 Revised  January 2004 Published  March 2004

This paper is concerned with the existence of almost periodic solutions of neutral functional differential equations of the form $\frac{d}{dt}Dx_t = Lx_t+f(t)$, where $D,$ $L$ are bounded linear operators from $\mathcal C$ :$ = C([-r, \quad 0],\quad \mathbb C^n )$ to $\mathbb C^n$, $f$ is an almost (quasi) periodic function. We prove that if the set of imaginary solutions of the characteristic equations is bounded and the equation has a bounded, uniformly continuous solution, then it has an almost (quasi) periodic solution with the same set of Fourier exponents as $f$.
Keywords: quasi periodic solution., almost periodic solution, Neutral functional differential equation.
Mathematics Subject Classification: 34K14, 34K0.
Citation: Nguyen Minh Man, Nguyen Van Minh. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Communications on Pure & Applied Analysis, 2004, 3 (2) : 291-300. doi: 10.3934/cpaa.2004.3.291
[1]

Yongkun Li, Pan Wang. Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 463-473. doi: 10.3934/dcdss.2017022
[2]

Yingte Sun, Xiaoping Yuan. Quasi-periodic solution of quasi-linear fifth-order KdV equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6241-6285. doi: 10.3934/dcds.2018268
[3]

Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281
[4]

Changrong Zhu, Bin Long. The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3793-3808. doi: 10.3934/dcdsb.2016121
[5]

Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1057-1067. doi: 10.3934/dcds.2005.13.1057
[6]

Xiao Wang, Zhaohui Yang, Xiongwei Liu. Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6123-6138. doi: 10.3934/dcds.2017263
[7]

John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91-101. doi: 10.3934/proc.2011.2011.91
[8]

Chunhong Li, Jiaowan Luo. Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3299-3318. doi: 10.3934/dcdsb.2018321
[9]

Xianhua Huang. Almost periodic and periodic solutions of certain dissipative delay differential equations. Conference Publications, 1998, 1998 (Special) : 301-313. doi: 10.3934/proc.1998.1998.301
[10]

Tomás Caraballo, David Cheban. Almost periodic and almost automorphic solutions of linear differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1857-1882. doi: 10.3934/dcds.2013.33.1857
[11]

Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167
[12]

Tomás Caraballo, Gábor Kiss. Attractivity for neutral functional differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1793-1804. doi: 10.3934/dcdsb.2013.18.1793
[13]

Hernán R. Henríquez, Claudio Cuevas, Alejandro Caicedo. Asymptotically periodic solutions of neutral partial differential equations with infinite delay. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2031-2068. doi: 10.3934/cpaa.2013.12.2031
[14]

Miguel V. S. Frasson, Patricia H. Tacuri. Asymptotic behaviour of solutions to linear neutral delay differential equations with periodic coefficients. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1105-1117. doi: 10.3934/cpaa.2014.13.1105
[15]

Changchun Liu, Hui Tang. Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions. Evolution Equations & Control Theory, 2017, 6 (2) : 219-237. doi: 10.3934/eect.2017012
[16]

Benjamin B. Kennedy. A periodic solution with non-simple oscillation for an equation with state-dependent delay and strictly monotonic negative feedback. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 47-66. doi: 10.3934/dcdss.2020003
[17]

Ernest Fontich, Rafael de la Llave, Yannick Sire. A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Electronic Research Announcements, 2009, 16: 9-22. doi: 10.3934/era.2009.16.9
[18]

Weigu Li, Jaume Llibre, Hao Wu. Polynomial and linearized normal forms for almost periodic differential systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 345-360. doi: 10.3934/dcds.2016.36.345
[19]

Yong Li, Zhenxin Liu, Wenhe Wang. Almost periodic solutions and stable solutions for stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5927-5944. doi: 10.3934/dcdsb.2019113
[20]

Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences