摘要
讨论了一类伴有边界摄动的非线性奇摄动四阶微分方程三点边值问题.在适当的条件下,利用摄动理论和微分不等式技巧证明了解的存在性,给出了其解及其导数的任意n阶一致有效渐近展开式.
Under appropriate conditions, a class of nonlinear singularly perturbed threepoints boundary value problem with boundary perturbation for fourth order differential equation is considered. Using the theories for perturbation and the differential inequalities, the existence of solution is proved. The uniformly valid asymptotic expansions of the solution and its derivations for arbitrary -th order are given.
出处
《应用数学学报》
CSCD
北大核心
2008年第2期231-238,共8页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(No．10471039)
浙江省自然科学基金(No．Y604127)
上海市教育委员会E-研究院建设计划(No．E03004)资助项目．
关键词
奇摄动
非线性
微分不等式
渐近展开式
singularly perturbation, nonlinear, differential inequality,asymptotic expansion
