On ground state of non local Schrodinger operators

2016/01/06 by Yuri Kondratiev, Kondratiev, Yuri, Stanislav Molchanov +7
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #47A10 #47D06 #60J35 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math-ph #math.FA #math.MP #msc:47A10 #msc:47D06 #msc:60J35

paper · pdf · doi:10.48550/arxiv.1601.01136

openalex publication_date 2016/01/06 · arxiv created 2016/01/28 · arxiv updated 2016/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a ground state of a non local Schrodinger operator associated with an evolution equation for the density of population in the stochastic contact model in continuum with inhomogeneous mortality rates. We found a new effect in this model, when even in the high dimensional case the existence of a small positive perturbation of a special form (so-called, small paradise) implies the appearance of the ground state. We consider the problem in the Banach space of bounded continuous functions C_b (R^d) and in the Hilbert space L²(R^d).

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