Multiple solutions for a class of $p(x)$-curl systems arising in electromagnetism

Abstract

In this paper, we study the existence of solutions for a class of of $p(x)$-curl systems arising in electromagnetism.  Under suitable conditions on the nonlinearities, we obtain at least two non-trivial solutions for the problem by using the mountain pass theorem combined with the Ekeland variational principle. Our main result in this paper complements and extends some earlier ones concerning the $p(x)$-curl operator in [4, 21].