×

zbMATH — the first resource for mathematics

Instability of nonautonomous differential systems. (English) Zbl 0992.34034
Summary: The author shows that the existence of an \((h,k)\)-dichotomy for \(x'=A(t)x\) yields an analysis of the instability of the null solution to the nonautonomous linear system \(y'=A(t)y+ f(t,y)\), \(f(t,0)=0\), where \(x'=A(t)x\) does not satisfy the conditions of Coppel’s theorem on instability.

MSC:
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
PDF BibTeX XML Cite