具有非线性边界条件的二阶非线性系统的奇摄动

Singular Perturbation of Second Order Nonlinear Systems with Nonlinear Boundary Conditions

本文研究具有非线性边界条件的二阶非线性系统的奇摄动。在适当的假设下,利用渐近分析和指数二分法以及泛函分析的不动点原理, 证明了解的存在唯一性并给出解的直到O(ε^(N+1))阶的一致有效渐近展开式。

In this paper the singular perturbation of second order nonlinear systems with nonlinear boundary conditions is discussed. Under suitable assumptions, by using the methods of asymptotic analysis and exponential dichotomy and the principle of fixed point of functional analysis, the existence and uniqueness of solution are proved. In addition, the uniformly valid asymptotic expansion of solution till O(ε^(N+1)) is given as well.