右端是Carath odory函数的二阶微分方程的周期边值问题

Periodic Boundary Value Problems for Second Order Differential Equations With Carath odory Functions

考虑周期边值问题-u″=f(t,u,u′),u(0)=u(2π),u′(0)=u′(2π),其中f满足Carath odory条件。进一步假设f满足Nagumo条件和Lipschitz条件,推广上、下解法和单调迭代方法,得到了介于下、上解之间的解及最大和最小解的存在性。

The periodic boundary value problem - u＂ = f（ t, u, u′ ）, u （0） = u （2π）, u′ （0） = u′ （2π）, where f satisfies Carathrodory condition is studied. The supposition is that f satisfies Nuguma condition and Lipschitz condition, the method of lower and upper solutions and monotone iterative technique to obtain the existence of solutions between lower and upper solutions and maximal and minimal solutions is generalized.