2009, 2009(Special): 315-321. doi: 10.3934/proc.2009.2009.315

Stability properties and existence of almost periodic solutions of volterra difference equations

1. 

Department of Information Science, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan

Received  July 2008 Revised  April 2009 Published  September 2009

In order to obtain the existence of periodic and almost periodic solutions of Volterra difference equation: $ x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s,x(n+s),x(n)) $, we consider certain two stability properties, which are referred to as (K, $ \rho $)-weakly uniformly asymptotically stable and (K, $ \rho $)-uniformly asymptotically stable.
Citation: Yoshihiro Hamaya. Stability properties and existence of almost periodic solutions of volterra difference equations. Conference Publications, 2009, 2009 (Special) : 315-321. doi: 10.3934/proc.2009.2009.315
[1]

Tomás Caraballo, David Cheban. Almost periodic and asymptotically almost periodic solutions of Liénard equations. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 703-717. doi: 10.3934/dcdsb.2011.16.703

[2]

Ewa Schmeidel, Karol Gajda, Tomasz Gronek. On the existence of weighted asymptotically constant solutions of Volterra difference equations of nonconvolution type. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2681-2690. doi: 10.3934/dcdsb.2014.19.2681

[3]

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

[4]

Denis Pennequin. Existence of almost periodic solutions of discrete time equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 51-60. doi: 10.3934/dcds.2001.7.51

[5]

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

[6]

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

[7]

Paolo Perfetti. Hamiltonian equations on $\mathbb{T}^\infty$ and almost-periodic solutions. Conference Publications, 2001, 2001 (Special) : 303-309. doi: 10.3934/proc.2001.2001.303

[8]

Małgorzata Migda, Ewa Schmeidel, Małgorzata Zdanowicz. Periodic solutions of a $2$-dimensional system of neutral difference equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 359-367. doi: 10.3934/dcdsb.2018024

[9]

Luis Barreira, Claudia Valls. Stable manifolds with optimal regularity for difference equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1537-1555. doi: 10.3934/dcds.2012.32.1537

[10]

Vera Ignatenko. Homoclinic and stable periodic solutions for differential delay equations from physiology. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3637-3661. doi: 10.3934/dcds.2018157

[11]

Peter Giesl, Martin Rasmussen. A note on almost periodic variational equations. Communications on Pure & Applied Analysis, 2011, 10 (3) : 983-994. doi: 10.3934/cpaa.2011.10.983

[12]

Anna Cima, Armengol Gasull, Francesc Mañosas. Global linearization of periodic difference equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1575-1595. doi: 10.3934/dcds.2012.32.1575

[13]

Tongren Ding, Hai Huang, Fabio Zanolin. A priori bounds and periodic solutions for a class of planar systems with applications to Lotka-Volterra equations. Discrete & Continuous Dynamical Systems - A, 1995, 1 (1) : 103-117. doi: 10.3934/dcds.1995.1.103

[14]

Gaston N'Guerekata. On weak-almost periodic mild solutions of some linear abstract differential equations. Conference Publications, 2003, 2003 (Special) : 672-677. doi: 10.3934/proc.2003.2003.672

[15]

Reinhard Farwig, Yasushi Taniuchi. Uniqueness of backward asymptotically almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1215-1224. doi: 10.3934/dcdss.2013.6.1215

[16]

Sorin Micu, Ademir F. Pazoto. Almost periodic solutions for a weakly dissipated hybrid system. Mathematical Control & Related Fields, 2014, 4 (1) : 101-113. doi: 10.3934/mcrf.2014.4.101

[17]

Anatoli F. Ivanov, Sergei Trofimchuk. Periodic solutions and their stability of a differential-difference equation. Conference Publications, 2009, 2009 (Special) : 385-393. doi: 10.3934/proc.2009.2009.385

[18]

A. Aschwanden, A. Schulze-Halberg, D. Stoffer. Stable periodic solutions for delay equations with positive feedback - a computer-assisted proof. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 721-736. doi: 10.3934/dcds.2006.14.721

[19]

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

[20]

M. R. Arias, R. Benítez. Properties of solutions for nonlinear Volterra integral equations. Conference Publications, 2003, 2003 (Special) : 42-47. doi: 10.3934/proc.2003.2003.42

 Impact Factor: 

Metrics

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

Other articles
by authors

[Back to Top]