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)=μg(x)|u|p(x)−2u+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.