We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208-233, 2005) to study the structure of positive solutions to the equation epsilon(m) Delta(m)u - u(m-1) + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of RN (N >/= 2). First, we study subcritical case for 2 < m < N and show that after passing by a sequence positive solutions go to a constant in C(1, alpha) sense as epsilon --> infinity. Second, we study the critical case for 1 < m < N and prove that there is a uniform upper bound independent of epsilon in [1, infinity) for the least-energy solutions. Third, we show that in the critical case for 1 < m infinity.

中文翻译：

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关于一类拟线性椭圆诺依曼问题解的结构。第二部分。

我们继续我们的工作 (Y. Li, C. Zhao in J Differ Equ 212:208-233, 2005) 研究方程 epsilon(m) Delta(m)u - u(m-1) 正解的结构+ f(u) = 0，在 RN (N >/= 2) 的光滑有界域中具有齐次 Neumann 边界条件。首先，我们研究 2 < m < N 的亚临界情况，并表明在通过序列后，正解在 C(1, alpha) 意义上成为 epsilon --> 无穷大的常数。其次，我们研究了 1 < m < N 的临界情况，并证明对于最小能量解，在 [1, infinity) 中存在独立于 epsilon 的统一上限。第三，我们证明在 1 < m无穷大的临界情况下。