Global bifurcation results on degenerate quasilinear elliptic systems

In this paper we prove certain bifurcation results for the following degenerate quasilinear system − ▽ ( ν 1 ( x ) | ▽ u | p − 2 ▽ u ) = λ a ( x ) | u | p − 2 u + λ b ( x ) | u | α | v | β v + f ( x , λ , u , v ) , − ▽ ( ν 2 ( x ) | ▽ u | p − 2 ▽ u ) = λ d ( x ) | v | q − 2 v + λ b ( x ) | u | α | v | β u + g ( x , λ , u , v ) , x ∈ Ω , u | ∂ Ω = v | ∂ Ω = 0 , where Ω is a bounded and connected subset of R N , with N ≥ 2 . This is achieved by applying topological degree and global bifurcation theory (in the sense of Rabinowitz).