Singular elliptic problems: Existence, non-existence and boundary behavior

We deal with the existence, uniqueness and boundary behavior of positive solutions of the semilinear elliptic equation -Delta u = rho a(x)g(u) + lambda b(x) f (u) in Omega, under Dirichlet boundary conditions, where Omega subset of R-N is a bounded domain with smooth boundary partial derivative Omega, a, b, g, f are continuous non-negative real valued functions. The main feature here is that either g or f (or both of them) are singular at 0 in the sense that g(t), f (t) ->(t -> 0) infinity and rho, lambda >= 0 are parameters. Our results require no symmetry from either a or b and no monotonicity on f or g. Penalty arguments as well as variational principles are exploited. (c) 2006 Elsevier Ltd. All rights reserved.