Calculus of Variations and Geometric Measure Theory

V. Felli - D. Mukherjee - R. Ognibene

On fractional multi-singular Schrödinger operators: positivity and localization of binding

created by ognibene on 15 Oct 2021


Published Paper

Inserted: 15 oct 2021

Journal: Journal of Functional Analysis
Year: 2020

ArXiv: 1905.05534 PDF


In this work we investigate positivity properties of nonlocal Schrödinger type operators, driven by the fractional Laplacian, with multipolar, critical, and locally homogeneous potentials. On one hand, we develop a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions, while, on the other hand, we study the localization of binding for this kind of potentials. Combining these two tools and performing an inductive procedure on the number of poles, we establish necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding Schrödinger operator.