Positive Periodic Solution of a Class of Nonlinear Second-OrderDifferential Equations
一类非线性二阶常微分方程的正周期解

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.