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Asymptotic relationship between solutions of two linear differential systems. (English) Zbl 0944.34030
Summary: Here, new generalized notions are defined: \(\Psi \)-boundedness and \(\Psi \)-asymptotic equivalence, where \(\Psi \) is a complex continuous nonsingular \(n\times n\)-matrix. The \(\Psi \)-asymptotic equivalence of linear differential systems \(\mathbf{y}'= \text\textbf{A}(t)\text\textbf{y}\) and \(\mathbf{x}'=\text\textbf{A}(t)\text\textbf{x}+\text\textbf{B}(t)\text\textbf{x}\) is proved when the fundamental matrix of \(\mathbf{y}'=\text\textbf{A}(t)\text\textbf{y}\) is \(\Psi \)-bounded.
MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
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