Large solutions of semilinear elliptic equations with a gradient term: Existence and boundary behavior

摘要

In this paper, we study the existence and boundary behavior of solutions to boundary blow-up elliptic problems Δu = b(x)f(u)(1 + |λu| ~q), u ≥ 0, x ∈ Ω, u|_(?Ω) = ∞, where is a bounded domain with smooth boundary in ?~N, q ∈ (0, 2], b ∈ C~α(ω?) which is positive in Ω, may be vanishing on the boundary, and f is normalised regularly varying at infinity with positive index p and p + q > 1.