Geodesic
On constant coefficient PDE systems and intersection multiplicities
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 2, pp. 108-114

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In this paper we consider the concept of the multiplicity of intersection points of plane algebraic curves $p,q=0,$ based on partial differential operators. We evaluate the exact number of maximal linearly independent differential conditions of degree $k$ for all $k\ge 0.$ On the other hand, this gives the exact number of maximal linearly independent polynomial and polynomial-exponential solutions, of a given degree $k,$ for homogeneous PDE system $p(D)f=0,$ $q(D)f=0.$
Keywords: intersection point, multiplicity, PDE system. 
N. K. Vardanyan. On constant coefficient PDE systems and intersection multiplicities. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 2, pp. 108-114. http://geodesic.mathdoc.fr/item/UZERU_2020_54_2_a4/
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[1] M. G. Marinari, H. M. Möller, T. Mora, “On Multiplicities in Polynomial System Solving”, Trans. Amer. Math. Soc., 348 (1996), 3283–3321 | DOI | MR | Zbl

[2] H. A. Hakopian, “A Multivariate Analog of Fundamental Theorem of Algebra and Hermite Interpolation”, Proceedings of the International Conference on Constructive Theory of Functions (Varna, June 19-23), ed. Bojanov B. D., Darba, Sofia, 2002, 1–18 | MR

[3] H. A. Hakopian, M. G. Tonoyan, “Partial Differential Analogs of Ordinary Differential Equations and Systems”, New York J. Math., 10 (2004), 89–116 | MR | Zbl

[4] R. J. Walker, Algebraic Curves, Springer–Verlag, 1978 | MR | Zbl

[5] H. A. Hakopian, M. G. Tonoyan, “On a Multivariate Theory”, Approximation Theory, A Volume Dedicated to Blagovest Sendov, ed. Bojanov B.D., Darba, Sofia, 2002, 212–230 | MR | Zbl

[6] G. S. Avagyan, “On Multiplicity of Intersection Point of Two Plane Algebraic Curves”, Contemp. Math. Anal., 45 (2010), 123–127 | DOI | MR | Zbl