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arXiv · 1601.01136

On ground state of non local Schrodinger operators

Yuri Kondratiev·Stanislav Molchanov·Sergey Pirogov·Elena Zhizhina
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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 $L^2(R^d)$.

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Yuri Kondratiev, Stanislav Molchanov, Sergey Pirogov, Elena Zhizhina. 2016-01-28. On ground state of non local Schrodinger operators. https://arxiv.org/abs/1601.01136

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