Geodesic
The Hilbert polynomial for systems of linear partial differential equations with analytic coefficients
Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 153-169

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We consider systems of linear partial differential equations with analytic coefficients and discuss existence and uniqueness theorems for their formal and analytic solutions. Using elementary methods, we define and describe an analogue of the Hilbert polynomial for such systems. 
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     author = {A. G. Khovanskii and S. P. Chulkov},
     title = {The {Hilbert} polynomial for systems of linear partial differential equations with analytic coefficients},
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     number = {1},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a6/}
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A. G. Khovanskii; S. P. Chulkov. The Hilbert polynomial for systems of linear partial differential equations with analytic coefficients. Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 153-169. http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a6/