Global bifurcation for nonlinear equations

Using a bifurcation result on noncompact branches of solutions in an abstract setting, we establish the existence of global bifurcation for the following nonlinear equation

−div(a|∇u|^p−2∇u)−_μ0b|u|^p−2u=q(λ,x,u,∇u)$-\text{div}\left(a{\left|\nabla u\right|}^{p-2}\nabla u\right)-{\mu }_{0}b{\left|u\right|}^{p-2}u=q(\lambda ,x,u,\nabla u)$

subject to Dirichlet boundary conditions under certain assumptions on a,b$a,b$ and q$q$ when _μ0${\mu }_0$ is not an eigenvalue of the above divergence form.