This note introduces a class of nonlinear Neumann problems on balls expanding with the radii tending toward infinity. Performing singular perturbation arguments, we establish the corresponding concentration phenomenon and refined asymptotic expansions with the precise first two-order terms. In doing so, we obtain the nontrivial boundary structure of solutions with effects coming from the nonlinear Neumann boundary condition and the boundary mean curvature varied with expanding domains.

中文翻译：

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半径趋于无穷大的球在Neumann问题中的非平凡边界结构

本说明介绍了随着半径趋于无穷大而扩大的球上的一类非线性诺伊曼问题。通过执行奇异摄动参数，我们建立了相应的集中现象，并利用精确的前两个二阶项完善了渐近展开。这样做，我们获得了具有非线性非线性诺伊曼边界条件和边界平均曲率随扩展域而变化的效应的非平凡边界结构。