| 超二次条件下差分方程的周期解 |
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| 引用本文： | 孟青. 超二次条件下差分方程的周期解[J]. 宿州学院学报, 2011, 26(8): 11-14. DOI: 10.3969/j.issn.1673-2006.2011.08.004 |
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| 作者姓名： | 孟青 |
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| 作者单位： | 东南大学数学系 江苏南京 210096;宿城第一中学 安徽宿州 234000 |
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| 摘 要： | 研究了二阶差分方程△（p（t）△u（t-1））＋△↓W（t，u（t））=0周期解的存在性，其中W（t，u）=-K（t，u）＋F（t，u）。假设K满足“夹逼”条件和F在原点与无穷远处是超二次的，分别用环绕定理和山路引理得到了多重或无穷多周期解，推广了某些已知的结果。
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| 关 键 词： | 差分方程 周期解 超二次 环绕定理 山路引理 |
Periodic Solutions for Difference Equations under Superquadratic Condition |
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| MENG Qing. Periodic Solutions for Difference Equations under Superquadratic Condition[J]. Journal of Shuzhou College, 2011, 26(8): 11-14. DOI: 10.3969/j.issn.1673-2006.2011.08.004 |
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| Authors: | MENG Qing |
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| Affiliation: | MENG Qing1,21.Department of Mathematics,Southeast University,Nanjing,210096,2.SuCheng No.1 Middle School,Suzhou Anhui,234000,China |
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| Abstract: | This paper analyzes the existence of periodic solutions for the second order difference equations-Δ(p(t)Δu(t-1))+/W(t,u(t))=0,where W(t,u)=-K(t,u)+F(t,u).Assuming that K satisfies the "pinching" condition and is superquadratic at zero and at infinity,multiple periodic solutions and infinitely many solutions are obtained respectively with the linking theorem and Mountain Pass lemma.The results provide a generalization for some known ones. |
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| Keywords: | difference equations periodic solutions superquadratic linking theorem Mountain Pass lemma |
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