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

Abstract

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: Delta _{p} u=b(x)f(u), u>0, xin varOmega, u|_{partial varOmega }=infty , where Ω is a bounded domain with smooth boundary in mathbb{R}^{N} (Ngeq 2), p>1, b in C^{alpha }(bar{varOmega }) which is positive in Ω and may be vanishing on the boundary. The absorption term f is normalized regularly varying at infinity with index sigma >p-1. The results extend some previous findings of D. Repovš (J. Math. Anal. Appl. 395:78-85, 2012) in a certain sense.