15 Sep 2015; IMS (UiTø), room TEKN 2.020. 14:15-15:15.

Elena Zhizhina (Institute for Information Transmission Problems, RAS, Moscow)

“Ground state for non local Schrodinger operator” (joint work with Yuri Kondratiev, Sergey Pirogov and Stanislav Molchanov)

We study a discrete spectrum of a non local Schrodinger operator associated with an evolution equation for the density of population in the stochastic contact model in continuum with an inhomogeneous mortality. 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 $L^2(R^d)$.