%0 Journal Article
%T Infinitely Many Solutions of Boundary Value Problems for a Classof Second-Order Ordinary Differential Equations<br>一类二阶常微分方程边值问题的无穷多个解
%A SHU Xiaobao
%A <br>舒小保
%J 系统科学与数学
%D 2008
%I 
%X By means of variational structure and $Z_2$ group index theory, infinitely many solutions of boundary value problems for second-order ordinary differential equations $$\arraycolsep=1.5pt \left\{\begin{array}{lcl}\displaystyle u'(t)-u(t)+ f(t,u(t))=0,\quad 0<t<1,\displaystyle u'(0)=0 ,\displaystyle \alpha_1 u(1)+ u'(1)=0,\end{array} \right. $$ are obtained, where $\alpha_1>-\frac{1}{2}$.
%K Variational structure
%K $Z_2$ group index theory
%K boundary value problems<br>变分原理
%K Z2不变群指标
%K 边值问题.
%K 二阶
%K 微分方程边值问题
%K 多个解
%K DIFFERENTIAL
%K EQUATIONS
%K ORDINARY
%K CLASS
%K BOUNDARY
%K VALUE
%K PROBLEMS
%K 充分条件
%K 存在
%K 指标研究
%K 不变群
%K 变分原理
%K 利用
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=614B254E93683EAB39B406F73ADA0315&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=CA4FD0336C81A37A&sid=76AA6C908A024FF6&eid=ACABFD5AC576697D&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=10