About Solutions of Nonlinear Algebraic System with Two Variables
Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 32-37
Received: Jan. 25, 2013; Published: Feb. 20, 2013
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Author
Rakhshanda Dzhabarzadeh, İnstitute Mathematics and Mechanics of NAN of Azerbaijan, Baku
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Abstract
For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced. At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
Keywords
Algebraic, Spectral, Resultant, Nonlinear
To cite this article
Rakhshanda Dzhabarzadeh, About Solutions of Nonlinear Algebraic System with Two Variables, Pure and Applied Mathematics Journal. Vol. 2, No. 1, 2013, pp. 32-37. doi: 10.11648/j.pamj.20130201.15
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