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Sibirsk. Mat. Zh., 2012, Volume 53, Number 6, Pages 1385–1390 (Mi smj2390)  

This article is cited in 1 scientific paper (total in 1 paper)

Existence and nonuniqueness of solutions to a functional-differential equation

A. I. Noarov

Institute of Numerical Mathematics, Moscow, Russia

Abstract: We examine the functional-differential equation $\Delta u(\boldsymbol x)-\operatorname{div}(u(H(\boldsymbol x))\mathbf f(\boldsymbol x))=0$ on a torus which is a generalization of the stationary Fokker–Planck equation. Under sufficiently general assumptions on the vector field $\mathbf f$ and the map $H$, we prove the existence of a nontrivial solution. In some cases the subspace of solutions is established to be multidimensional.

Keywords: stationary Fokker–Planck equation, deviating argument.

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English version:
Siberian Mathematical Journal, 2012, 53:6, 1115–1118

Bibliographic databases:

UDC: 517.956.22
Received: 19.01.2012

Citation: A. I. Noarov, “Existence and nonuniqueness of solutions to a functional-differential equation”, Sibirsk. Mat. Zh., 53:6 (2012), 1385–1390; Siberian Math. J., 53:6 (2012), 1115–1118

Citation in format AMSBIB
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\paper Existence and nonuniqueness of solutions to a~functional-differential equation
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\pages 1115--1118
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Noarov, “Nontrivial solvability of elliptic equations in divergence form with complex coefficients”, Siberian Math. J., 55:3 (2014), 465–470  mathnet  crossref  mathscinet  isi  elib  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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