摘要
本文先提出一类三阶非线性微分方程的两点边值问题,利用Nagumo条件和上下解的技巧,讨论上述问题解的存在性和解的估计;然后,运用该结果,研究相应的奇摄动问题。在适当的条件下。
In this paper, a boundary value problem of third order nonlinear differential equation is presented and the existence of its solutions is discussed by using lower and upper solutions and a Nagumo condition. Then the results obtained above are applied to the corresponding singularly perturbed problem. Finally, under some suitable conditions, the uniformly valid asymptotic expansion to any degree of precision is given to the solution of the singularly perturbed proglem on the entire interval.
基金
国家自然科学基金
关键词
非线性
微分方程
边值问题
奇摄动
Singular perturbation
Boundary value problem
Nonlinear differential equation
Upper and lower solutions
