Asymptotic relationship between solutions of two linear differential systems

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

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