一类三阶积分边值问题的两个迭代正解

Two iterative positive solutions to a class of third order integral boundary value problem

利用上下解结合单调迭代方法建立一类三阶积分边值问题两个迭代正解的存在性。通过建立相应线性积分边值问题的格林函数得到解的表达式,并讨论其格林函数性质。将该边值问题解的存在性问题转化为锥上算子的不动点问题,并建立该算子的全连续性。在不用假设上下解存在的情况下,通过构造上下解并应用单调迭代方法建立该边值问题正解的存在性,同时得到逼近正解的迭代格式。最后给出了结论的具体应用。

The existence of two iterative positive solutions to a class of third-order integral boundary value problem is established by using the upper and lower solutions and monotone iterative method.The expression of the solutions is obtained by establishing the Green function of the corresponding linear integral boundary value problem,and the properties of the Green function are discussed.And the existence problem of the solutions to the boundary value problem is transformed into the fixed point problem to an operator defined on a cone,and the complete continuity of the operator is estab-lished.Then the existence of positive solutions to the boundary value problem is proved by con-structing the upper and lower solutions and the monotone iterative method without assuming the existence of the upper and lower solutions,and the iterative format of approximating the positive solutions is also obtained.Finally,a concrete application is given for the main result.