Bounded solutions of finite lifetime to differential equations in Banach spaces

Rafael Dahmen, Helge Glockner

Consider a smooth vector field $f:{\mathbb{R}}^n\to {\mathbb{R}}^n$ and a maximal solution $\gamma :]a,b[\to {\mathbb{R}}^n$ to the ordinary differential equation $x^{\prime }=f(x)$. It…