论文标题
准线性批判性理论和格林在图表上的功能
Quasi-Linear Criticality Theory and Green's Functions on Graphs
论文作者
论文摘要
我们研究了与准线性Schrödinger运算符在无限图上相关的能量功能，并通过Green的功能，最小生长和能力的谐波功能来发展（子）关键的特征。我们证明了Agmon-Allegretto-Piepenbrink定理的准线性版本，该版本说，当且仅当具有正谐音函数时，能量功能是非负的。此外，我们表明，仅当能量功能是亚临界值时，就存在绿色的功能。比较原则和最大原则是证明的主要工具。
We study energy functionals associated with quasi-linear Schrödinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a quasi-linear version of the Agmon-Allegretto-Piepenbrink theorem, which says that the energy functional is non-negative if and only if there is a positive superharmonic function. Furthermore, we show that a Green's function exists if and only if the energy functional is subcritical. Comparison principles and maximum principles are the main tools in the proofs.
