Singular elliptic problems with convection term in anisotropic media

We are concerned with singular elliptic problems of the form −∆u ± p(d(x))g(u) = λf(x, u) + μ|∇u|a in Ω, where Ω is a smooth bounded domain in R , d(x) = dist(x, ∂Ω), λ > 0, μ ∈ R, 0 < a ≤ 2, and f, k are nonnegative and nondecreasing functions. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p(d(x)), the convection term |∇u|a, and the singular nonlinearity g, we establish various existence and nonexistence results. 2000 Mathematics Subject Classification: 35B50, 35J65, 58J55.