Existence and multiplicity of solutions for p(x)-curl systems arising in electromagnetism

In this paper, we study the existence and multiplicity of solutions to a class of p(x)-curl systems arising in electromagnetism. The results obtained in this paper extend several contributions concerning the p-curl operator and we focus on new existence results which are due to the presence of variable exponent. To our best knowledge, our results are new even in the semilinear case.