Algebrization of Nonautonomous Differential Equations

[摘要] Given a planar system of nonautonomous ordinary differential equations, dw/dt=F(t,w), conditions are given for the existence of an associative commutative unital algebra A with unit e and a function H:??R2×R2?R2 on an open set ? such that F(t,w)=H(te,w) and the maps H1(?)=H(?,?) and H2(?)=H(?,?) are Lorch differentiable with respect to A for all (?,?)??, where ? and ? represent variables in A. Under these conditions the solutions ?(?) of the differential equation d?/d?=H(?,?) over A define solutions (x(t),y(t))=?(te) of the planar system.

[学科分类] 应用数学