Lane-Emden-Fowler equations with convection and singular potential

We are concerned with singular elliptic problems of the form -Delta u +/- p(d(x))g(u) = lambda f(x, u) + mu vertical bar del u vertical bar(a) in Omega, where Omega is a smooth bounded domain in R-N, d(x) = dist(x, partial derivative Omega), lambda > 0, mu epsilon R, 0 < a <= 2, and f is a nondecreasing function. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Omega 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 vertical bar del u vertical bar(a), and the singular nonlinearity g, we establish various existence and nonexistence results. (c) 2007 Elsevier Masson SAS. All rights reserved.