# zbMATH — the first resource for mathematics

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
Full Text: