Asymptotic boundary estimates for solutions to the p-Laplacian with infinite boundary values.

In this paper, by using Karamata regular variation theory and the method of upper and lower solutions, we mainly study the second order expansion of solutions to the following p-Laplacian problems: Δ p u = b (x) f (u) , u > 0 , x ∈ Ω , u | ∂ Ω = ∞ , where Ω is a bounded domain with smooth boundary in R N (N ≥ 2) , p > 1 , b ∈ C α (Ω ¯) which is positive in Ω and may be vanishing on the boundary. The absorption term f is normalized regularly varying at infinity with index σ > p − 1 . The results extend some previous findings of D. Repovš (J. Math. Anal. Appl. 395:78-85, 2012) in a certain sense. [ABSTRACT FROM AUTHOR]