Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (2): 172-183.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.003

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Existence of Three Positive Periodic Solutions of Neutral Nonlinear Functional Difference Equations

  

  1. Department of Mathematics, Shaoyang University
  • Received:2013-04-21 Online:2015-06-30 Published:2020-11-23
  • About author:LIU Xing-yuan(1963-), male, native of Shaoyang, Hunan, a professor of Shaoyang University, engages in function differential equations.
  • Supported by:
    Supported by the Natural Science Foundation of Hunan Province(12JJ6006); Supported by the Science Foundation of Department of Science and Technology of Hunan Province(2012FJ3107);

Abstract: This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson. 

Key words: positive periodic solution, functional difference equation, fixed-point theorem

CLC Number: