In this paper, by constructing new comparison functions, we mainly study the boundary behavior of solutions to boundary blow-up elliptic problems for more general nonlinearities f (which may be rapidly varying at infinity) △ ∞ u = b ( x ) f ( u ) $riangle_{infty} u =b(x)f(u)$ , x ∈ Ω $xin Omega $ , u | ∂ Ω = + ∞ $u|_{partial Omega }=+infty$ , where Ω is a bounded domain with smooth boundary in R N $mathbb{R}^{N}$ , and b ∈ C ( Ω ¯ ) $b in C(ar{Omega })$ which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary.
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机译：在本文中，通过构造新的比较函数，我们主要研究边界爆破椭圆问题的解的边界行为，以获取更一般的非线性f（可能在无限远处迅速变化）△∞u = b（x）f（u ）$ triangle _ { infty} u = b（x）f（u）$，x∈Ω$ x in Omega $，u | ΩΩ= +∞$ u | _ { partial Omega} = + infty $，其中Ω是RN $ mathbb {R} ^ {N} $中具有光滑边界的有界域，b∈C（Ω ¯）$ b in C（ bar { Omega}）$在Ω中为正，可能在边界上消失并在边界附近快速变化。
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