两参数奇摄动非线性非局部高阶椭圆型方程边值问题的渐近解

摘要

研究了一类非线性非局部高阶椭圆型方程奇摄动边值问题。在适当的条件下，首先求出了原问题的外部解。然后利用多重尺度变量、合成展开法构造出解的第一、第二边界层项，并得到解的形式渐近展开式。最后，利用微分不等式理论，研究了两参数边值问题解的渐近展开式。导出了几个有关的不等式。讨论了原问题存在一个解和解的一致有效渐近估计式。%The singularly perturbed boundary value problem for a class of nonlinear nonlocal elliptic equation of higher order was considered.Under suitable conditions,the outer solution of the original problem was obtained.Then,applying the multiple scales variable and the method of component expansion,the first and second boundary layer corrective terms were constructed and the formal asymptotic expansion was obtained. Finally, applying the theory of differential inequalities the asymptotic expansion of a solution for the boundary value problem with two parameters was studied.Some relational inequalities were educed.And the existence of the solution for the original problem and the uniformly valid asymptotic estimation were discussed.