ON THE EXISTING CONDITIONS OF BOUNDARY SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS SYSTEMS
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Abstract
In the previous studies, the problem about the asymptotical stability substitution of the linear differential systems in the case of a given linear operator's spectrum has been shown to be stable (Nguyen, 2013; Konyaev, & Nguyen, 2014).
This paper investigates the existing conditions of boundary solutions of non-autonomous linear differential equations systems
satisfied original condition
with
in the case of a given linear operator's spectrum that is not stable. It is a harder problem. Then it will be used to solve the solution of the linear differential equations systems which is equivalent to system (1).
Besides, with the result-based approach by Nguyen (2013), the solution of the boundary problem with disturbed diffusion coefficient has been solved.
satisfied initial condition
and the result is illustrated by an specific example.
Keywords
linear differential equation systems, boundary solution, matrix function, spectrum of matrices, half elemental structure
Article Details
References
Konyaev Yu. A., & Nguyen, V. K. (2014). Spectral analysis of some classes of non-autonomous systems with periodic and polynomially periodic matrices. Bulletin of the National Research Nuclear University MEPhI. 3(3), 1-7.
Lancaster P. (1978). Matrix Theory. Moscow, Russian Federation, M.: Nauka.
Nguyen, V. K. (2013). Analytical methods for studying the stability of linear and quasilinear systems with a polynomially periodic matrix. Vestnik RUDN, series: Mathematics. Informatics. Physics, (4), Moscow, 18-23.
Nguyen, V. K. (2017). Research about the asymptotical stability substitution of the linear differential systems with periodic coefficients on the basis of spectral method. Ho Chi Minh City University of Education Journal of Science, 14(6), 157-164.