| 非线性二阶差分系统周期解的多重性 |
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| 引用本文： | 陈永刚,胡哲.非线性二阶差分系统周期解的多重性[J].甘肃科学学报,2010,22(3):44-49. |
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| 作者姓名： | 陈永刚 胡哲 |
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| 作者单位： | 中国石油大学,数学与计算科学学院,山东,东营,257061 |
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| 摘 要： | 变分方法是研究非线性差分方程周期解存在性的一种新的并且行之有效的方法.运用乘积空间上的环绕定理1]证明二阶非线性差分系统{-Δ2un-1=μ1uαn1+f1(n,un)+λh1(n,un,vn),n∈M-Δ2vn-1=μ2vαn2+f2(n,vn)+λh2(n,un,vn),n∈M其中αi∈(0,1),i=1,2,至少存在3个非平凡的周期解.
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| 关 键 词： | 非线性差分系统 环绕 非平凡周期解 |
Multiplicity of Periodic Solutions of Second Order Nonlinear Difference Systems |
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| CHEN Yong-gang,HU Zhe.Multiplicity of Periodic Solutions of Second Order Nonlinear Difference Systems[J].Journal of Gansu Sciences,2010,22(3):44-49. |
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| Authors: | CHEN Yong-gang HU Zhe |
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| Institution: | (School of Mathematics and Computational Science,China University of Petroleum,Dongying 257061,China) |
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| Abstract: | The variational method is an effective method for studying the existence of periodic solutions for nonlinear difference equations.The linking theorem on product space is applied to study the following second order nonlinear difference systems{-Δ2un-1=μ1uα1n＋f1（n,un）＋λh1（n,un,vn）,n∈M -Δ2vn-1=μ2vα2n＋f2（n,vn）＋λh2（n,un,vn）,n∈M where αi∈（0,1）,i=1,2.At least three nontrivial periodic solutions exist. |
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| Keywords: | nonlinear difference system linking nontrivial periodic solution |
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