摘要
研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数.
We study the successive iteration of positive solution for a 2nth Lidstone boundary value problem where the nonlinear term depends on all even-order derivatives. By considering the ＂heights＂ of nonlinear term on some bounded sets and applying monotone iterative technique we construct a successive iterative process. This iterative process starts off with a polynomial and is feasible. Applying this result we obtain the iterative method of m positive solutions where m is an arbitrary natural number.
出处
《应用泛函分析学报》
CSCD
2006年第2期110-117,共8页
Acta Analysis Functionalis Applicata
关键词
Lidstone边值问题
高阶常微分方程
正解
逐次迭代
Lidstone boundary value problem
higher-order ordinary differential equation
positive solution
successive iteration
