Singular quasilinear elliptic problems on unbounded domains

We prove the existence of a solution between an ordered pair of sub and supersolutions for singular quasilinear elliptic problems on unbounded domains. Further, we use this result to establish the existence of a positive solution to the problem { -Delta(p)u = lambda K(x)f(u) in B-1(c), u = 0 on partial derivative B-1, u(x) -> 0 as vertical bar x vertical bar -> infinity, where B-1(c) = {x is an element of R-n | vertical bar x vertical bar > 1}, Delta(p)u = div(vertical bar del u vertical bar(p-2)del u), 1 < p < n, lambda is a positive parameter, K belongs to a class of functions which satisfy certain decay assumptions and f belongs to a class of (p - 1)-subhomogeneous functions which may be singular at the origin, namely lim(s -> 0+) f (s) = -infinity. Our methods can be also applied to establish a similar existence result when the domain is entire R-n. (C) 2014 Elsevier Ltd. All rights reserved.