Dear all, consider now a solution

$\displaystyle x(t):\ [0,\infty)\to R$

to an ode

$\displaystyle x'=f(x)$

If $\displaystyle x(t)$ is bounded. Show $\displaystyle \lim_{t\to\infty}x(t)=c$

for some constant $\displaystyle c$

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- Aug 6th 2011, 08:07 PMxinglongdadaWhy bounded ode solution tends to a constant
Dear all, consider now a solution

$\displaystyle x(t):\ [0,\infty)\to R$

to an ode

$\displaystyle x'=f(x)$

If $\displaystyle x(t)$ is bounded. Show $\displaystyle \lim_{t\to\infty}x(t)=c$

for some constant $\displaystyle c$ - Aug 7th 2011, 03:07 AMchisigmaRe: Why bounded ode solution tends to a constant
- Aug 7th 2011, 11:04 AMFernandoRevillaRe: Why bounded ode solution tends to a constant
- Oct 16th 2011, 06:32 PMxinglongdadaRe: Why bounded ode solution tends to a constant
Indeed, this is a very nice counterexample...Good luck