Geodesic
Comparison of powers of differential polynomials
Eurasian mathematical journal, Tome 14 (2023) no. 4, pp. 23-46

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Necessary and sufficient conditions are obtained for a polynomial $P$ to be more powerful then a polynomial $Q$. These conditions are formulated in terms of the orders of generalized-homogeneous sub-polynomials, corresponding to these polynomials, and the multiplicity of their zeros. Applying these results, conditions are obtained, under which a monomial $\xi^v$ for a certain set of multi-indices $v\in\mathfrak{R}^*$ can be estimated via terms of a given degenerate polynomial $P$. 
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     author = {H. G. Ghazaryan},
     title = {Comparison of powers of differential polynomials},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_4_a3/}
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H. G. Ghazaryan. Comparison of powers of differential polynomials. Eurasian mathematical journal, Tome 14 (2023) no. 4, pp. 23-46. http://geodesic.mathdoc.fr/item/EMJ_2023_14_4_a3/