2 00 5 On a class of sublinear singular elliptic problems with convection term

We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −∆u + K(x)g(u) + |∇u| a = λf (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N (N ≥ 2) is a smooth bounded domain, 0 < a ≤ 2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term |∇u| a. Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations.