Geodesic
Asymptotic relationship between solutions of two linear differential systems
Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 163-175

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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.
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.
DOI : 10.21136/MB.1998.126305
Classification : 34A30, 34C11, 34E10
Keywords: ${\bold\Psi}$-boundedness; ${\bold\Psi}$-asymptotic equivalence 
Miklo, Jozef. Asymptotic relationship between solutions of two linear differential systems. Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 163-175. doi: 10.21136/MB.1998.126305
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