Abstract

We study the existence and multiplicity of positive solutions of the non-homogeneous elliptic equation -Δu = q(|x|)f(u) for |x| > 1 and x ∈ ℝN,} u(x) = a for |x| = 1, u(x) → b as |x| → +∞, where N ≥ 3, the nonlinearity f is superlinear at both zero and infinity, q is a non-trivial, non-negative function, and a and b are non-negative parameters. A typical model is given by f(u) = up, with p > 1. © 2006 The Royal Society of Edinburgh.