We consider Robin problems driven by the anisotropic p-Laplace operator and with a logistic reaction. Our analysis covers superdiffusive, subdiffusive and equidiffusive equations. We examine all three cases, and we prove multiplicity properties of positive solutions (superdiffusive case) and uniqueness (subdiffusive and equidiffusive cases). The equidiffusive equation is studied only in the context of isotropic operators. We explain why the more general case cannot be treated.

中文翻译：

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Logistic反应的各向异性Robin问题

我们考虑由各向异性p -Laplace算子驱动并具有对数反应的Robin问题。我们的分析涵盖了超扩散，次扩散和等扩散方程。我们研究了所有三种情况，并证明了正解（超扩散情况）和唯一性（亚扩散和等扩散情况）的多重性。仅在各向同性算子的上下文中研究等价扩散方程。我们解释了为什么无法处理更一般的情况。