Timeline for Does there exist a comparison principle for vector differential equations?
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| when toggle format | what | by | license | comment | |
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| Jun 21, 2017 at 12:49 | comment | added | Igor Khavkine | Your hypothesis $\|F(x)\|\leq \|G(x)\|$ is too weak to say something very useful, as illustrated in the answer by Kostya below. However, if you allow $x$ to take values in some space with a (sufficiently smooth) partial order relation $\le$ and $F(x) \le G(x)$ for all $x$, then you essentially have the same conclusions as in the scalar case. An example of such a space is $(\mathbb{R}^n,\le)$, where $(a_1,\ldots,a_n) \le (b_1,\ldots,b_n)$ if and only if $a_i \le b_i$ for all $i$. | |
| Jun 21, 2017 at 12:22 | history | edited | Neil Strickland | CC BY-SA 3.0 |
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| Jun 21, 2017 at 10:26 | answer | added | Kostya_I | timeline score: 1 | |
| Jun 21, 2017 at 9:36 | history | asked | W. Nyway | CC BY-SA 3.0 |