Boundary blow-up solutions of p-Laplacian elliptic equations with lower order terms

Abstract

We study the existence, uniqueness, and asymptotic behavior of blow-up solutions for a general quasilinear elliptic equation of the type -Δ pu = a(x)u m-b(x)f(u) with p > 1 and 0 < m < p-1. The main technical tool is a new comparison principle that enables us to extend arguments for semilinear equations to quasilinear ones. Indeed, this paper is an attempt to generalize all available results for the semilinear case with p = 2 to the quasilinear case with p > 1. © 2011 Springer Basel AG.