%0 Journal Article
%T Positive Periodic Solution of a Class of Nonlinear Second-OrderDifferential Equations<br>一类非线性二阶常微分方程的正周期解
%A YAO Qingliu
%A <br>姚庆六
%J 系统科学与数学
%D 2008
%I 
%X The positive solutions are considered for the nonlinear second-order ordinary differential equation $u^{\prime \prime }(t)=f(t,u(t))$ with the boundary condition $u(0)=u(2\pi),~u^{\prime}(0)=u^{\prime}(2\pi)$. Because there is not Green function for the equation, the usual methods are invalid. By applying suitable transform technique and fixed point theorem on cone, the existence of $n$ positive solutions is proved for the equation, where $n$ is an arbitrary natural number.
%K Second-order ordinary differential equation
%K periodic boundary value problem
%K positive solution
%K existence
%K multiplicity<br>二阶常微分方程
%K 周期边值问题
%K 正解
%K 存在性
%K 多解性.
%K 非线性
%K 二阶常微分方程
%K 正周期解
%K DIFFERENTIAL
%K EQUATIONS
%K NONLINEAR
%K CLASS
%K PERIODIC
%K SOLUTION
%K 自然数
%K 存在性
%K 边值问题
%K 定理证明
%K 不动点
%K 转换技巧
%K 利用
%K 方法
%K 函数
%K Green
%K 正解
%K 边界条件
%K 考察
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=9CA54475B43CF601B421ED6F0359C2EC&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=CA4FD0336C81A37A&sid=6E5881F2FFE5E466&eid=B28963F0DCA783C7&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=12