On semilinear Δλ-Laplace equation

We prove some existence, nonexistence and regularity results for the boundary value problem Δλu+f(u)=0in Ω,u∣∂Ω=0, where ΩΩ is a bounded subset of RNRN, N≥2N≥2, and ΔλΔλ is a ΔλΔλ-Laplacian, i.e. a “degenerate” elliptic operator of the kind Δλ:=∑i=1N∂xi(λi2(x)∂xi),λ=(λ1,…,λN). Together with some assumptions made in Franchi and Lanconelli (1984) [1], the family λλ is supposed to verify a condition making ΔλΔλ homogeneous of degree two with respect to a group of dilations in RNRN.