﻿ 关于Lyness型差分方程的C1不变曲线 The C1 Invariant Curve of Lyness Type Difference Equations

Pure Mathematics
Vol.06 No.03(2016), Article ID:17689,11 pages
10.12677/PM.2016.63040

The C1 Invariant Curve of Lyness Type Difference Equations

Miaoqiao Pan, Ruiqi Chen, Zongzhao Mo, Fuge Pan, Yezhi Li, Ying Zhang

School of Mathematics and Computational Science, Lingnan Normal University, Zhanjiang Guangdong

Received: May 6th, 2016; accepted: May 20th, 2016; published: May 27th, 2016

ABSTRACT

In this paper, by using the Schauder fixed point theorem and Banach fixed point theorem, also the related properties of the compact convex subset, the existence, uniqueness; stability and retention property of the C1 invariant curves of Lyness type difference equations are researched.

Keywords:Lyness Type Difference Equations, Invariant Curves, Existence, Uniqueness, Stability, Retention Property

1. 引言

(1.1)

(1.2)

2. 预备知识

，显然是一个Banach空间，其中对，且

(i)

(ii)

(iii)

(iv)

(i)

(ii)

(iii)

(iv)

(v)

，由条件，得

(i)

(ii)

(iii)

(iv)

(v)

3. 主要结果

(E1)

(E2)

(1) 算子是自同胚的

，有：

(2)在范数下是连续的

，那么就有

(3.11)

(3) 类似于文献 [6] ，一个紧凸子集。

(E3)：

4. 举例应用

[例]设，且是连续函数，且有，则方程内有唯一的解，即差分方程上有唯一的不变曲线。

The C1 Invariant Curve of Lyness Type Difference Equations[J]. 理论数学, 2016, 06(03): 261-271. http://dx.doi.org/10.12677/PM.2016.63040

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