Scholarlink

<p>We study energy functionals associated with quasi-linear Schrödinger operators on infinite graphs, and develop characterisations of criticality via Green’s functions, harmonic functions of minimal growth and capacities. We prove 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 positive minimal 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quasi-linear criticality theory and Green’s functions on graphs

  • 期刊论文

  • 发表日期：

    2025年11月12日

查看全文
  • Florian Fischer

摘要

We study energy functionals associated with quasi-linear Schrödinger operators on infinite graphs, and develop characterisations of criticality via Green’s functions, harmonic functions of minimal growth and capacities. We prove 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 positive minimal 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.