| 临界群与二阶差分方程解的多重性 |
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| 引用本文： | 李小艳,刘进生.临界群与二阶差分方程解的多重性[J].数学的实践与认识,2012,42(11):255-260. |
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| 作者姓名： | 李小艳 刘进生 |
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| 作者单位： | 太原理工大学数学学院,山西太原,030024 |
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| 摘 要： | 研究了一类二阶非线性差分方程两点边值问题解的多重性.当该问题的非线性项在无穷远点具有特殊的渐近线性性质时,利用变分方法,结合临界群与Morse理论,同时考虑正、负能量泛函的临界点,不论该问题是否发生共振,均证明了它至少存在两个非零解.
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| 关 键 词： | 差分方程 多重性 变分方法 临界群 Morse理论 |
The Critical Groups and the Multiplicity of Solutions for Second-Order Difference Equations |
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| LI Xiao-yan
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LIU Jin-sheng.The Critical Groups and the Multiplicity of Solutions for Second-Order Difference Equations[J].Mathematics in Practice and Theory,2012,42(11):255-260. |
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| Authors: | LI Xiao-yan LIU Jin-sheng |
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| Institution: | (College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | In this paper,we study the multiplicity of solutions for a two-point boundary value problem of second-order nonlinear difference equations.By using variational method, combining with critical groups and Morse theory,considering critical points of both the positive and negative energy functional,when nonlinear term of the problem has a special asymptotic property at the infinite point,we prove the problem has at least two non-zero solutions,no matter whether resonance is happened. |
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| Keywords: | difference equation multiplicity variational method critical groups Morse theory |
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