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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) \(\triangle_{\infty} u =b(x)f(u)\), \(x\in \Omega \), \(u|_{\partial \Omega }=+\infty\), where Ω is a bounded domain with smooth boundary in \(\mathbb{R}^{N}\), and \(b \in C(\bar{\Omega })\) which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary.

The exact asymptotic behavior of blow-up solutions to a highly degenerate elliptic problem