Asymptotic boundary estimates for solutions to the p-Laplacian with infinite boundary values
Ling Mi · Boundary Value Problems · 2019
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, x\in \varOmega, u|_{\partial \varOmega }=\infty $ , where Ω is a bounded domain with smooth boundary in $\mathbb{R}^{N} (N\geq 2)$ , $p>1$ , $b \in C^{\alpha }(\bar{\varOmega })$ 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.