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.

在这份手稿中，考虑了涉及拉普拉斯算子的系统的解决方案的存在性和多样性，这些解决方案与电流变流体、图像处理、机器人技术和空间技术等多种应用有关。在一般条件下，通过将子超解与凸集中的最小化参数相结合，可以获得所考虑系统的第一个解。此外，考虑到 Ambrosetti-Rabinowitz 类型的条件并应用 Mountain Pass 定理，证明了该问题存在第二个解。这些假设允许考虑范围广泛的非线性，本文的结果改进和补充了最近的一些贡献。