Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains

We study the problem of the existence and nonexistence of positive solutions to the superlinear second-order divergence type elliptic equation with measurable coefficients -del(.)a(.)delu = u(P) (*), p > 1, in an unbounded cone-like domain G subset of R-N (N greater than or equal to 3). We prove that the critical exponent p*(a, G) = inf{p > 1: (*) has a positive supersolution at infinity in G} for a nontrivial cone-like domain is always in (1, N/N-2) and depends both on the geometry of the domain G and the coefficients a of the equation. (C) 2004 Elsevier SAS. All rights reserved.