Differential equations over polynomially bounded o-minimal structures
Differential equations over polynomially bounded o-minimal structures
We investigate the asymptotic behavior at $+\infty$ of non-oscillatory solutions to differential equations $yâ=G(t,y), t>a$, where $G\colon \mathbb {R}^{1+l}\to \mathbb {R}^l$ is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.