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Volume 18,     Number 1,     Spring 2010

 

DIMENSION PROBLEMS FOR
NONHOMOGENEOUS DIFFERENTIAL
EQUATIONS
JAMES MULDOWNEY AND EVGENIA SAMUYLOVA

Abstract. The codimension of stable subspaces of certain function spaces arising from nonhomogeneous linear differential equations is considered. The history of the problem begins with a result on second order linear scalar equations by a French mathematician Milloux in 1934 and continues with Hartman, Coppel, Macki and Muldowney as well as many others in the second half of the twentieth century. The PhD dissertation of Wang (2008) discusses the question in infinite dimensional spaces. This and earlier studies deal exclusively with homogeneous systems. Related questions for nonhomogeneous systems of linear differential equations are considered here. The evolution of k-volumes expressed as exterior products of solutions plays a major role in the study.

 

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