含多个小参数的高阶拟线性椭圆型方程一般边值问题的奇摄动

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Singular Perturbation of General Boundary Value Problem for Higher-Order Quasilinear Elliptic Equation Involving Many Small Parameters

摘要: 本文应用М.Н.Вишик和Л.А.Люстерник^[1]的渐近方法以及泛函分析的不动点原理研究了方程与边界摄动相结合的高阶拟线性椭圆型方程一般边值问题的奇摄动,证明了摄动问题解的存在且唯一,给出解的渐近展开式和有关的余项估计.

Abstract: In this paper applyiag M. I. Visik and L. A. Lpusternik's^[1] asymptotic method and principle of fixed point of functional analysis, we study the singular perturbation of general boundary value problem for higher order quasilinear elliptic equation in the case of boundary perturbation combined with equation perturbation. We prove the existence and uniqueness of solution for perturbed problem. We give its asymptotic approximation and estimation of related remainder term.

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