%0 Journal Article
%T The Existence of a Nontrivial Solution for Biharmonic Equation<br>重调和方程非平凡解的存在性
%A Tang Chunxia
%A Zhang Zhengjie
%A <br>唐春霞
%A 张正杰
%J 数学物理学报(A辑)
%D 2008
%I 
%X The paper mainly studies biharmonic equation in $R^N(N>4)$ as$$\left\{\begin{array}{ll} \Delta^2 u+\lambda u=\overline{f}(x,u);\\ \lim\limits_{|x|\rightarrow\infty}u(x)=0;\\u\in{H^2}(R^N),\hspace{0.1cm}x\in{R^N }.\end{array}\right.$$ For studying it, the authors change it to the biharmonic equation with a perturbation in $R^N(N>4)$ as$$\left\{\begin{array}{ll} \Delta^2 u+\lambda u=f(u)+\varepsilon g(x,u);\\ \lim\limits_{|x|\rightarrow\infty}u(x)=0;\\u\in{H^2}(R^N),\hspace{0.1cm}x\in{R^N } \end{array}\right.$$and use the perturbation method to study it (where $f(u)=\lim\limits_{|x|\longrightarrow \infty}\overline{f}(x,u),\varepsilon g(x,u)=\overline{f}(x,u)-f(u),\varepsilon$ is a small constant). The authors can prove the existence of nontrivial solutions of the above question under some conditions.
%K Existencezz
%K Biharmonic equationzz
%K Perturbativezz<br>存在性
%K 重调和方程
%K 扰动.
%K 重调和方程
%K 非平凡解
%K 存在性
%K Biharmonic
%K Equation
%K Nontrivial
%K Solution
%K 问题
%K 条件
%K 常数
%K 任意小
%K 扰动方法
%K 运用
%K 扰动项
%K 方程转化
%K 研究
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=08EEE456F0D8FB7F2BD6A96E8EC3326F&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=0B39A22176CE99FB&sid=80BD0A2EF8664214&eid=FDC7AF55F77D8CD4&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=11