Existence of solutions for nonhomogeneous A-harmonic equations with variable growth

We study the following nonhomogeneous A -harmonic equations: d A (x, d u (x)) + B (x, u (x)) = 0, x , u (x) = 0, x , where n is a bounded and convex Lipschitz domain, A (x, d u (x)) and B (x, u (x)) satisfy some p (x) -growth conditions, respectively. We obtain the existence of weak solutions for the above equations in subspace 0 1, p (x) (, l - 1) of W 0 1, p (x) (, l - 1).