On the weak solvability of a class of variable exponent systems

We use a variational approach based on the mountain-pass theorem to prove the existence of weak solutions for nonlinear variable exponent systems with homogeneous Dirichlet boundary conditions. The class of systems discussed here is governed by Leray-Lions type operators which, under sufficiently relaxed hypotheses, are covering as particular cases generalized Laplace, mean curvature, and capillarity operators, as well as various combinations of them. Thus, our main result yields a unified framework for several nonlinear models connected to a large number of potential applications.