一类n阶方程Robin问题的存在性定理和对解的估计

THE EXISTENCE AND ESTIMATION OF THE SOLUTION OF THE ROBIN PROBLEM FOR A CLASS OF nTH ORDER EQUATION

在文献[1]中,Kelley利用上、下解证明了一类n阶方程Dirichlet问题解的存在性,Howes讨论了这类问题解的零阶近似。而本文先利用上、下解证明了这类问题中的Robin问题的解的存在性,再利用微分不等式理论研究了奇摄动Robin问题的包括边界层在内的解的任意阶近似。

In this paper we first consider the existence of the solution for a class of nth order Robin problem,then discuss the existence and estimation of the solution of the Robin problem for a class of singularly perturbed nth order equation,using the theory of differential inequalities we obtain the arbitrary order uniformly valid asymptotic estimation of the solution,including boundary layer,of the original problem.