具有混合单调非线性项的四阶微分方程两点边值问题

Two Point Boundary Value Problem of Fourth Order Differential Equation with Mixed Monotone Nonlinear Terms

讨论了一类具有混合单调非线性项的四阶微分方程两点边值问题,运用一类混合单调算子的不动点定理及"和型"非线性算子的不动点定理,结合单调迭代技巧和格林函数的性质,获得方程正解存在且唯一的充分条件,并构造两个迭代序列收敛于此唯一解.最后,给出具体的例子验证了定理的正确性.

In this paper,we discuss a class of two point boundary value problem of fourth order differential equation with mixed monotone nonlinear term.By using a class of fixed point theorems of mixed monotone operator and a sum type nonlinear operator,combining with monotone iterative technique and the properties of Green function,we obtain the sufficient conditions which guarantee the existence and uniqueness of positive solution,also we provide iterative sequences for approximating the solution.At last,a concrete example is listed to testify the theorem.