Existence of Positive Solutions for a Class of Variable Exponent Elliptic Systems - Ala, S.; Afrouzi, G. A. (MATHEMATICA SCANDINAVICA, 2016)
We consider the system of differential equations \[ cases -Δ_p(x)u=λ^p(x)f(u,v)&in Ω, -Δ_q(x)v=μ^q(x)g(u,v)&in Ω, u=v=0&on Ω,cases \] where Ω R^N is a bounded domain with C^2 boundary Ω,1<p(x),q(x)C^1(Ω) are functions. Δ_p(x)u=div olimits(| abla u|^p(x)-2 abla u) is called p(x)-Laplacian. We discuss the existence of a positive solution via sub-super solutions.