Abstract This paper concerns with a class of elliptic anisotropic Dirichlet problems depending of one real parameter on bounded Euclidean domains. Our approach is based on variational and topological methods. More concretely, along the paper we show the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci and Serrin theorem in addition to a local minimum result for differentiable functionals due to Ricceri. This abstract approach has been developed for equations on Carnot groups; see [15] .

中文翻译：

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一些各向异性狄利克雷问题的存在性结果

摘要 本文研究了一类椭圆各向异性狄利克雷问题，该问题取决于有界欧几里得域上的一个实参数。我们的方法基于变分和拓扑方法。更具体地说，在论文中，我们通过使用著名的 Pucci 和 Serrin 定理的直接结果以及由于 Ricceri 导致的可微泛函的局部最小值结果，证明了所处理问题至少存在两个弱解。这种抽象方法是为卡诺群方程开发的；见[15]。