论文标题
存在用于奇异扰动的非线性非自动传播问题的解决方案
Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem
论文作者
论文摘要
在本文中，我们分析了拉普拉斯方程的边界价值问题，其在较小的尺寸$ε$的边界上的非线性非自动传输条件。我们表明，该问题的解决方案的$ε$足够小，我们研究了特定解决方案家族对$ε$的依赖性。通过采用一种功能分析方法，我们证明将$ε$（适当限制）的地图可以用真实的分析功能表示。
In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $ε$. We show that the problem has solutions for $ε$ small enough and we investigate the dependence of a specific family of solutions upon $ε$. By adopting a functional analytic approach we prove that the map which takes $ε$ to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.
