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.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
北大核心
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)
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
singular perturbation
boundary value problem
nonlinear vector equation
diagonalization method
