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MATHEMATICA BOHEMICA, Vol. 123, No. 2, pp. 163-175 (1998)
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Asymptotic relationship between solutions of two linear differential systems

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Jozef Miklo

* Jozef Miklo*, Katedra matematiky Strojnickej fakulty STU, nam. Slobody 17, 812 31 Bratislava, Slovakia

**Abstract:** 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.

**Keywords:** ${\bold\Psi}$-boundedness, ${\bold\Psi}$-asymptotic equivalence

**Classification (MSC2000):** 34A30, 34E

**Full text of the article:**

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