Bifurcation results for a class of p(x)-Laplacian equations

In this paper, we study the following p(x)-Laplacian equation: {−div(|∇u|p(x)−2∇u)+λ|u|p(x)−2u=f(x,u)x∈Ω,u(x)=0x∈∂Ω, where Ω⊂RN is bounded, λ≥0. Under suitable assumptions, we obtain the existence of global branches of solutions for the above problem via the subsolution-supersolution method.