论文标题
非本地准线性基态表示和批判性理论
A Non-Local Quasi-Linear Ground State Representation and Criticality Theory
论文作者
论文摘要
我们研究与非本地准线性Schrödinger运算符相关的能量功能，并开发基态表示。我们的主要重点是无限图，但我们也考虑了欧几里得空间中的非本地准线性schrödinger操作员。使用表示形式，我们在一般加权图上为准线性schrödinger操作员开发了批判性理论，并显示出耐力不平等的特征。作为应用程序，我们在图表上显示了Liouville比较原则。
We study energy functionals associated with non-local quasi-linear Schrödinger operators, and develop a ground state representation. Our main focus is on infinite graphs but we also consider non-local quasi-linear Schrödinger operators in the Euclidean space. Using the representation, we develop a criticality theory for quasi-linear Schrödinger operators on general weighted graphs, and show characterisations for a Hardy inequality to hold true. As an application, we show a Liouville comparison principle on graphs.
