Existence of boundary blow-up solutions for a quasilinear elliptic equation

Abstract

In this paper, the existence of solution for a class of quasilinear elliptic problem div(|∇ u| p−2 ∇ u)=a(x)f(u), u≥0 in Ω=B (the unit ball), with the boundary blow-up condition u| ∂Ω=+∞ is established, where a(x)∈C(Ω) blows up on ∂Ω,p>1 and f is assumed to satisfy (f 1) and (f 2). The results are obtained by using sub-supersolution methods.