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

LIU Xing-yuan

doi:10.13371/j.cnki.chin.q.j.m.2015.02.003

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 2: 172 - 183

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.003

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

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Department of Mathematics, Shaoyang University

LIU Xing-yuan(1963-), male, native of Shaoyang, Hunan, a professor of Shaoyang University, engages in function differential equations.

Received date: 2013-04-21

Online published: 2020-11-23

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)；

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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

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LIU Xing-yuan . Existence of Three Positive Periodic Solutions of Neutral Nonlinear Functional Difference Equations[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(2) : 172 -183 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.003

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