Recent content by Roger1

I find this, $arctan(x(t))+\int_{0}^{T}(x(s)-2)f(s)ds<\pi /2$. $x(t)$ is finite for all $t\geq 0$.

Here T, it is not necessarily finite. It is interesting to get an inequality of the form arctan(x(t))< $\frac{\pi}{2}$. for all $t\ge0$.

Let x(t) a positive function satisfied the following differential inequality $\frac{x'(t)}{1+{x(t)}^{2}}+x(t)f(t)<2f(t)$ , (1) with $0\leq t\leq T$ , $\arctan(0)<\frac{\pi }{2}$ and $f(t)$ is a positive function. Is x(t) bounded for all $T\geq 0$?