Asymptotics for singular solutions of quasilinear elliptic equations with absorption term

TL;DR

This paper analyzes the asymptotic behavior of positive blow-up solutions for a class of quasilinear elliptic equations with absorption, providing detailed boundary expansions using Karamata theory for various nonlinearities.

Contribution

It introduces a novel asymptotic expansion method near the boundary for solutions of quasilinear elliptic equations with absorption, covering broad nonlinearities of Keller-Osserman type.

Findings

First two terms of boundary expansion derived

Applicable to large classes of nonlinearities

Enhanced understanding of blow-up boundary solutions

Abstract

We are concerned with the asymptotic analysis of positive blow-up boundary solutions for a class of quasilinear elliptic equations with absorption term. By means of the Karamata theory we establish the first two terms in the expansion of the singular solution near the boundary. Our analysis includes large classes of nonlinearities of Keller-Osserman type.