| 一阶超线性时滞差分方程的周期解 |
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| 引用本文： | 郭丽芬,郭志明. 一阶超线性时滞差分方程的周期解[J]. 广州大学学报(综合版), 2014, 0(2): 19-23 |
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| 作者姓名： | 郭丽芬 郭志明 |
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| 作者单位： | 广州大学数学与信息科学学院,广东广州510006 |
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| 基金项目： | 国家自然科学基金重点资助项目（11031002）. |
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| 摘 要： | 应用临界点理论，主要研究一阶超线性时滞差分方程au（n）=-f（u（n—T））的非平凡周期解的存在性与多重性，其中u∈R，f∈C（R，R），T为给定的正整数．当f（u）在零点与无穷远点处满足超线性增长条件时，得到了上述方程以4T＋2为周期的非平凡周期解存在性与多解性的若干充分条件．
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| 关 键 词： | 时滞差分方程 周期解 临界点 环绕 |
Periodic solutions to first order superlinear delay difference equation |
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| GUO Li-fen,GUO Zhi-ming. Periodic solutions to first order superlinear delay difference equation[J]. Journal of Guangzhou University, 2014, 0(2): 19-23 |
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| Authors: | GUO Li-fen GUO Zhi-ming |
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| Affiliation: | (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China) |
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| Abstract: | By using critical point theory, the existence and multiplicity of nontrivial periodic solutions are investigated for first order superlinear delay difference equation △u（n） = -f（ u（n - T） ）, where u ∈ R, f∈ C（ R, R ） and T is a given positive integer. Some sufficient conditions are obtained for the existence and multiplicity of periodic solutions with period 4 T ＋ 2, when f（u） grows superlinearly both at zero and at infinity. |
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| Keywords: | delay difference equation periodic solution critical point linking methods |
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