带有非局部边界条件的非线性四阶奇异边值问题的对称正解(英文)  

Symmetric positive solution for nonlinear singular BVPs of fourth-order with nonlocal boundary conditions

作　　者：贺明阳[1] 么焕民[1] 

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025

出　　处：《黑龙江大学自然科学学报》2011年第3期352-359,共8页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Nature Science Foundation of Heilongjiang Province(A201015);the Scientific Research Foundation of the Education Department of Heilongjiang Province(11541098);the Doctorial Fund of Harbin Normal University(KGB200901)

摘　　要：在再生核空间中构造一个新的带有非局部边界条件的非线性四阶奇异边值问题的对称正解的迭代算法。证明近似解及其k(k=1,2,3,4)阶导函数一致收敛于精确解及其各阶导函数。给出的数值算例验证方法的有效性。所提出的算法对于求解线性与非线性积分边界问题是有效的。A new constructive iterative method is employed to obtain the symmetric positive solution for nonlinear singular BVPs of fourth-order with nonlocal boundary conditions in the reproducing kernel space.The approximate solution are proved to converge uniformly to the exact solution with all its k-order（k=1,2,3,4） derivatives.Numerical examples are given to verify the strength of the method.It is worthy to note that the new method can be used as a very accurate algorithm for solving linear and nonlinear integral boundary problems.

关 键 词：非线性 奇异 非局部边界条件 对称正解 再生核空间 

分 类 号：O241.8[理学—计算数学]