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 $\displaystyle c$
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 $\displaystyle c$