带有扰动的二阶周期可积边值问题解的存在唯一性及数值解(英文)

Existence,Uniqueness and Numerical Solution for Second-order Periodic-integrable Boundary Value Problems with Perturbation

本文讨论一类带有扰动的二阶周期可积边值问题,利用变分方法和已有结果得到了问题解的存在唯一性.结果表明,在某些条件下,扰动生成非平凡解;在另一些条件下,情况完全不同.同时,文章给出这类问题的的数值解法,称之为混合打靶法,并利用数值模拟显示出算法的有效性,所得结果是已有文献的进一步深入.

The existence and uniqueness of solutions for a second-order periodicintegrable boundary value problems with a perturbation was considered by variational method.The results show that the perturbation plays an important role under some conditions,and does not work under some other different conditions.On the other hand,the mixed-shooting method was established to find the numerical solution.This is a further discussion of the known results.