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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

3 votes
2 answers
129 views

ODEs whose finite-time solutions are not L^2 on their interval of definition

Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be analytic and consider the ODE $$x'(t)=f(x(t)).$$ It is well-known that if $(t_{min},t_{max})$ is the maximal domain of a solution $x$ and $t_{max}<\infty$, then …
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