Global bifurcation for a class of degenerate elliptic equations with variable exponents

We are concerned with the following nonlinear problem − div ( w ( x ) | ∇ u | p ( x ) − 2 ∇ u ) = μ g ( x ) | u | p ( x ) − 2 u + f ( λ , x , u , ∇ u ) in Ω subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the above divergence form. The purpose of this paper is to study the global behavior of the set of solutions for the above equation, by applying a bifurcation result for nonlinear operator equations.