| 二阶非齐次非线性差分方程与方程组的次调和周期解的多解性 |
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| 引用本文： | 张会凌.二阶非齐次非线性差分方程与方程组的次调和周期解的多解性[J].兰州大学学报(自然科学版),2007,43(1):119-125. |
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| 作者姓名： | 张会凌 |
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| 作者单位： | 甘肃联合大学数学与信息学院,甘肃 兰州,73000 |
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| 摘 要： | 通过应用由赵培浩等提出的乘积空间的环绕定理.提出了一种研究非线性差分方程及方程组的次调和周期解的存在性与多解性的新方法.对于二阶非齐次非线性差分方程组{-△2un-1=μ1 f1(n,un) λh1(n,un,vn), n∈z,一△2un-1=μ2 f2(n,vn) λh2(n,un,vn),n∈z,得到了一些新的结果.特别地,给出了此方程组存在至少两个非平凡周期解的充分条件.
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| 关 键 词： | 非线性差分方程与方程组 变分法 环绕 最小最大定理 非平凡周期解 |
| 文章编号： | 0455-2059（2007）01-0119-07 |
| 修稿时间： | 2006-09-01 |
Multiplicity of periodic and subharmonic solutions to second order nonhomogeneous nonlinear difference equations and systems |
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| ZHANG Hui-ling.Multiplicity of periodic and subharmonic solutions to second order nonhomogeneous nonlinear difference equations and systems[J].Journal of Lanzhou University(Natural Science),2007,43(1):119-125. |
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| Authors: | ZHANG Hui-ling |
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| Institution: | School of Mathematics and Information, Gansu Lianhe University, Lanzhou 730000, China |
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| Abstract: | By using the linking theorem on single space and on product space developed by Zhao et al, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for nonlinear difference equations and systems. For the second order nonhomogeneous nonlinear difference system some new results are obtained. In particular, sufficient conditions for the existence of two nontrivial period solutions are provided. |
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| Keywords: | nonlinear difference equation and systems variational argument linking minimax theorem nontrivial period solution |
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