三阶非线性向量常微分方程边值问题的奇摄动  

Singular perturbation of BVP for third-order nonlinear VDE

作　　者：林苏榕[1,2] 倪明康[2,3] 

机构地区：[1]福建广播电视大学计算机系,福州350003 [2]华东师范大学数学系、上海200062 [3]上海高校计算科学B研究院上海交通大学研究所,上海200030

出　　处：《华东师范大学学报（自然科学版）》2012年第1期138-150,共13页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11071075);上海市自然科学基金(10ZR1409200);上海市教育委员会E-研究院建设项目(E03004);福建广播电视大学科研课题(KY01194);福建省教育厅科技-项目(JA11288)

摘　　要：研究非线性三阶向量常微分方程的奇摄动边值问题.在一定的条件下,转变所给方程为对角化系统,然后去求解等价的积分方程,再用逐步逼近法和不动点原理,证得摄动问题解的存在并给出渐近估计.最后,给出了若干应用例子.The singularly perturbations for the vector boundary value problem of nonlinear thirdorder ordinary differential equations were studied. Under certain conditions, the given differential equation was transformed into a diagonalized system, and then the equivalent integral equations was solved. By using the method of succesive approximation and the theorem of fixed point, the existence of the solution of singular perturbation problem was proved and the asymptotic estimation was obtained. Finally, several examples of application were given.

关 键 词：奇异摄动 边值问题 非线性向量微分方程 对角化方法 

分 类 号：O175[理学—数学]