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In this manuscript, it is considered existence and multiplicity of solutions for a system involving the -Laplacian operator which are related to several applications such as electrorheological fluids, image processing, robotics and space technology. A first solution for the system considered is obtained, under general conditions, by combining sub-supersolutions with a minimization argument in convex sets. Additionally, considering an Ambrosetti-Rabinowitz type condition and applying the Mountain Pass Theorem it is proved the existence of a second solution for the problem. The hypotheses allow to consider an wide class of nonlinearities and the results in this paper improve and complement some recent contributions.

Multiplicity results for a system involving the p(x)- Laplacian operator