On the reduction of the degree of linear differential operators

Details On the reduction of the degree of linear differential operators On the reduction of the degree of linear differential operators

2010-03-02

arxiv.org/abs/1003.0629v1

Nonlinearity 24 (2011) 373-388

Mathematics

Classical Analysis and ODEs

Scientific paper

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.

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