This article is cited 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.

UDC: 517.956.22

Received: 19.01.2012

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

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