Multiparameter bifurcation and asymptotics for the singular Lane-Emden-Fowler equation with convection term

We establish some bifurcation results for the boundary value problem −∆u = g(u) + λ|∇u| + μf(x, u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R , λ, μ ≥ 0, 0 < p ≤ 2, f is nondecreasing with respect to the second variable, and g is unbounded around the origin. The asymptotic behaviour of the solution around the bifurcation point is also established, provided g(u) behaves like u around the origin, for some 0 < α < 1. Our approach relies on finding explicit suband super-solutions combined with various techniques related to the maximum principle for elliptic equations. The analysis we develop in this paper shows the key role played by the convection term |∇u|.