Global bifurcation results on degenerate quasilinear elliptic systems

In this paper we prove certain bifurcation results for the following degenerate quasilinear system −▽(ν1(x)|▽u|p−2▽u)=λa(x)|u|p−2u+λb(x)|u|α|v|βv+f(x,λ,u,v),−▽(ν1(x)|▽u|p−2▽u)=λa(x)|u|p−2u+λb(x)|u|α|v|βv+f(x,λ,u,v),−▽(ν2(x)|▽u|p−2▽u)=λd(x)|v|q−2v+λb(x)|u|α|v|βu+g(x,λ,u,v),x∈Ω,u|∂Ω=v|∂Ω=0, where ΩΩ is a bounded and connected subset of RNRN, with N≥2N≥2. This is achieved by applying topological degree and global bifurcation theory (in the sense of Rabinowitz).