Multiplicity of solutions for some Steklov problems involving the \lowercase{$(p(x)$-$q(x))$}-Laplace operator

In this paper, we use the variational method to study some Steklov problems involving the $p(x)$-$q(x)$-Laplace operator. Specifically, in the first part of this paper, we combine the mountain pass theorem with Ekeland's variational principle to prove the existence of two nontrivial weak solutions. Furthermore, in the second part of this work, we use the symmetric version of the mountain pass theorem to prove the existence of an infinite number of solutions to such problems.