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.
Felli, V., Mukherjee, D., Ognibene, R. (2020). On fractional multi-singular Schrödinger operators: Positivity and localization of binding. JOURNAL OF FUNCTIONAL ANALYSIS, 278(4) [10.1016/j.jfa.2019.108389].
On fractional multi-singular Schrödinger operators: Positivity and localization of binding
Felli V.
;Ognibene R.
2020
Abstract
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.File | Dimensione | Formato | |
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