边界与算子双摄动的四阶拟线性椭圆型方程的奇摄动

Singular Perturbation for A Class of Fourth-order Quasilinear Elliptic Equation with Boundary and Operator Double Perturbation

研究带有边界和算子双摄动的拟线性椭圆型方程的渐近解.在适当条件下利用边界层函数法和不动点定理证得解的存在性和唯一性,并给出解的渐近展开式和有关的余项估计.

The asymptotics solution of fourth-order quasilinear elliptic equation with boundary and operator double perturbation is studied. Under suitable conditions, by using the method of boundary layer function and the fixed point theorem, the existence and the uniqueness of solution are proved. The asymptotic expansion of solution and its estimation of related remainder term are given as well.