Bifurcation results for a class of image-Laplacian equations Original Research Article

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