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Of all publications in the section: 4
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Article
Alexander Pereskokov. Applicable Analysis. 2016. Vol. 95. No. 7. P. 1560-1569.

We consider the eigenvalue problem for a perturbed two-dimensional

resonance oscillator. The excitation potential is given by a Hartree-type

nonlinearity with a smooth self-action potential. We use asymptotic

formulas for the quantum averages to obtain asymptotic eigenvalues and

asymptotic eigenfunctions near the lower boundaries of spectral clusters

which are formed near the energy levels of the unperturbed operator.

Added: Mar 4, 2017
Article
Kondratiev Y., Molchanov S., Pirogov S. et al. Applicable Analysis. 2016.

We study a ground state of some non-local Schrödinger 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 (Formula presented.) and in the Hilbert space (Formula presented.). © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Added: Jul 6, 2016
Article
Molchanov S., Whitmeyer J. Applicable Analysis. 2015.

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Added: Jun 22, 2016
Article
Koralov L., Molchanov S., Vainberg B. Applicable Analysis. 2020.

We consider a mean-field model of a polymer with a spherically symmetric finitely supported potential. We describe how the typical size of the polymer depends on the two parameters: the temperature, which approaches the critical value, and the length of the polymer chain, which goes to infinity.

Added: Oct 28, 2020