Global bifurcation for nonlinear equations Original Research Article

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)−div(a|∇u|p−2∇u)−μ0b|u|p−2u=q(λ,x,u,∇u) Turn MathJax on subject to Dirichlet boundary conditions under certain assumptions on a,ba,b and qq when μ0μ0 is not an eigenvalue of the above divergence form.