Differential Equations by Viorel Barbu

Author:Viorel Barbu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.63)

where are the roots of the equation , and is an algebraic polynomial of degree at most , and is the multiplicity of the root .

Proof

Denote by a column of the matrix and by the characteristic polynomial of the matrix A, that is, . From Cayley’s theorem, we deduce that . Using the fact that satisfies (3.56), we deduce that the column satisfies the linear differential system with constant coefficients

where the differential operator P(D) is defined as in (3.38). Invoking Theorem 3.10, we deduce that the components of have the form (3.63).

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