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| 非线性时滞差分方程周期解的存在性 | |
| 引用本文： | 邢秋萍,王其如,郭志明.非线性时滞差分方程周期解的存在性[J].应用泛函分析学报,2012,14(1):61-70. |
| 作者姓名： | 邢秋萍 王其如 郭志明 |
| 作者单位： | 1. 广州大学土木工程学院,广州,510006 2. 中山大学数学与计算科学学院,广州,510275 3. 广州大学数学与信息科学学院,广州,510006 |
| 基金项目： | 国家自然科学基金(10871053,11031002);广州市教育局科技计划项目(62006) |
| 摘 要： | 主要研究一阶非线性时滞差分方程△x（n）=-f（x（n-T））的非平凡周期解的存在性与多解性．应用临界点理论，在，满足一定的增长性条件下，得到了上述方程存在非平凡周期解的一系列充分条件．另外，还通过若干例子阐明结论的可行性。 |
| 关 键 词： | 时滞差分方程 周期解 存在性 临界点理论 |
Existence of Periodic Solutions to Nonlinear Difference Equations with Delay |
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| XING Qiuping , WANG Qiru , GUO Zhiming.Existence of Periodic Solutions to Nonlinear Difference Equations with Delay[J].Acta Analysis Functionalis Applicata,2012,14(1):61-70. | |
| Authors: | XING Qiuping WANG Qiru GUO Zhiming |
| Institution: | 1.School of Civil Engineering,Guangzhou University,Guangzhou 510006,China 2.School of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou 510275,China 3.School of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China |
| Abstract: | This paper deals with the existence and multiplicity of nontrivial periodic solutions to the first order nonlinear difference equation with delay of the form△x(n)=-f(x(n-T)) By applying the critical point theory,several sufficient conditions are obtained for the periodic solutions to the equation above under the assumption that f satisfies certain growth conditions both at zero and at infinity.Some examples are given to illustrate the feasibility of the main results. |
| Keywords: | delay difference equation periodic solution existence the critical point theory |
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