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Difference and Differential Equations
Edited by: Saber Elaydi, Trinity University, San Antonio, TX, Gerry Ladas, University of Rhode Island, Kingston, RI, Jianhong Wu, York University, North York, ON, Canada, and Xingfu Zou, Memorial University of Newfoundland, St. John's, NL, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2004; 438 pp; hardcover
Volume: 42
ISBN-10: 0-8218-3354-5
ISBN-13: 978-0-8218-3354-4
List Price: US$131
Member Price: US$104.80
Order Code: FIC/42
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This volume contains papers from the 7th International Conference on Difference Equations held at Hunan University (Changsa, China), a satellite conference of ICM2002 Beijing. The volume captures the spirit of the meeting and includes peer-reviewed survey papers, research papers, and open problems and conjectures.

Articles cover stability, oscillation, chaos, symmetries, boundary value problems and bifurcations for discrete dynamical systems, difference-differential equations, and discretization of continuous systems.

The book presents state-of-the-art research in these important areas. It is suitable for graduate students and researchers in difference equations and related topics.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students and research mathematicians interested in differential equations and applications.

Table of Contents

Survey articles
  • H. Brunner -- The discretization of Volterra functional integral equations with proportional delays
  • J. M. Cushing -- The LPA model
  • X. Z. Qian and Z. C. Wang -- A survey on oscillation of linear delay difference equations
  • Y. Yi -- On almost automorphic oscillations
Research articles
  • R. M. Abu-Saris and K. I. Al-Dosary -- Complex exponential Vandermonde determinant with application to discrete boundary value problem
  • Y. Cao -- A convergence theorem related to iterative mean clustering
  • A. Chen and L. Huang -- Global attractivity in a model of bobwhite quail with delay
  • S. S. Cheng, C.-W. Chen, and T. Y. Wu -- Linear time discrete periodic diffusion networks
  • B. Dai, X. Qian, and L. Huang -- Convergence of solutions for a discrete-time system
  • T. Furumochi, S. Murakami, and Y. Nagabuchi -- Stabilities in Volterra difference equations on a Banach space
  • S. Guo and L. Huang -- Periodic oscillation for a class of delay difference systems
  • Z. Guo and J. Yu -- Applications of critical point theory to difference equations
  • D. Levi -- Lie symmetries for lattice equations
  • X. Li and Z. Wang -- Global attractivity for a logistic equation with piecewise constant arguments
  • X. Lin -- Bounded oscillation for a class of second order neutral delay difference equations
  • K. Liu and H. Zhang -- Asymptotic behavior in nonlinear discrete-time neural networks with delayed feedback
  • Y. Liu, L. Huang, and Z. Yuan -- Asymptotic behavior and periodicity of solutions for a difference equation with piecewise constant nonlinearity
  • Y. Liu, Z. Zhou, and W. Ge -- Positive solutions of a non-autonomous delay model of single population
  • H. Matsunaga -- Stability regions for a class of delay difference systems
  • M. Migda -- Oscillation and nonoscillation results for higher-order nonlinear difference equations
  • C. Pötzsche -- Stability of center fiber bundles for nonautonomous difference equations
  • R. J. Sacker and H. F. von Bremen -- Bifurcation of maps and cycling in genetic systems
  • E. Schmeidel -- Nonoscillation and oscillation theorems for a fourth order nonlinear difference equation
  • H. Sedaghat -- On the equation \(x_{n+1}=cx_{n}+f(x_{n}-x_{n-1})\)
  • C. Tian, J. Zhang, and Z. Ji -- Stability criteria for a kind of delay functional equation
  • L. Wang and X. Zou -- Exponential stability of delay difference equations with applications to neural networks
  • X. Wang and L. Liao -- Asymptotic behavior of solutions of linear difference-differential equations with oscillating coefficients
  • W. Wendi -- Analysis of a discrete predator-prey model
  • H.-W. Wu and Y.-T. Xu -- Oscillation for nonautonomous neutral difference equations with variable coefficients
  • Z. Yinggao -- Oscillation of higher-order nonlinear delay difference equations
  • Z. Yuan, L. Huang, and Z. Zhou -- Coexistence of multiple attractive periodic solutions in a discrete-time neural network
  • R. Y. Zhang, Z. C. Wang, and J. S. Yu -- Necessary and sufficient conditions for the existence of positive solutions of nonlinear difference equations
  • Z. Zhou and Q. Zhang -- Periodic solutions of a class of difference systems
  • H. Zhu and L. Huang -- Dynamic analysis of a discrete-time network of two neurons with delayed feedback
Open problems and conjectures
  • S. Elaydi -- Open problems and conjectures
  • H. Brunner -- Discretization of Volterra integral equations with weakly singular kernels
  • S. Elaydi -- Nonautonomous difference equations: Open problems and conjectures
  • E. A. Grove and G. Ladas -- On period-two solutions of \(x_{n+1} =\frac{\alpha + \beta x_{n}+\gamma x_{n-1}}{A + Bx_{n}+ C x_{n-1}}\)
  • R. J. Sacker and H. F. von Bremen -- Open problems on cycling in genetic systems
  • J. Wu -- On periodic solutions of systems of two difference equations
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