Article

 Title: Asymptotic relationship between solutions of two linear differential systems (English) Author: Miklo, Jozef Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 123 Issue: 2 Year: 1998 Pages: 163-175 Summary lang: English . Category: math . Summary: In this paper new generalized notions are defined: ${\bold\Psi}$-boundedness and ${\bold\Psi}$-asymptotic equivalence, where ${\bold\Psi}$ is a complex continuous nonsingular $n\times n$ matrix. The ${\bold\Psi}$-asymptotic equivalence of linear differential systems $y'= A(t) y$ and $x'= A(t) x+ B(t) x$ is proved when the fundamental matrix of $y'= A(t) y$ is ${\bold\Psi}$-bounded. (English) Keyword: ${\bold\Psi}$-boundedness Keyword: ${\bold\Psi}$-asymptotic equivalence MSC: 34A30 MSC: 34C11 MSC: 34E10 idZBL: Zbl 0944.34030 idMR: MR1673981 DOI: 10.21136/MB.1998.126305 . Date available: 2009-09-24T21:30:39Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/126305 . Reference: [1] R. Bellman: Stability Theory of Differential Equations.New York, 1953. Zbl 0053.24705, MR 0061235 Reference: [2] E. A. Coddington N. Levinson: Theory of Ordinary Differential Equations.New York, 1955. MR 0069338 Reference: [3] M. Greguš M. Švec V. Šeda: Ordinary Differential Equations.Bratislava, 1985. (In Slovak.) Reference: [4] A. Haščák: Asymptotic and integral equivalence of multivalued differential systems.Hiroshima Math. J. 20 (1990), no. 2, 425-442. MR 1063376, 10.32917/hmj/1206129191 Reference: [5] A. Haščák M. Švec: Integral equivalence of two systems of differential equations.Czechoslovak Math. J. 32 (1982), 423-436. MR 0669785 Reference: [6] M. Švec: Asymptotic relationship between solutions of two systems of differential equations.Czechoslovak Math. J. 2J, (1974), 44-58. MR 0348202 Reference: [7] M. Švec: Integral and asymptotic equivalence of two systems of differential equations.Equadiff 5. Proceedings of the Fifth Czechoslovak Conference on Differential Equations and Their Applications held in Bratislava 1981. Teubner, Leipzig, 1982, pp. 329-338. MR 0716002 .

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