$x,y:[0,1]\rightarrow\mathbb{R}$ are positive continuous functions. $y\left(p\right)$ is also monotone increasing (weakly). What are the conditions on $y$ so that there is $p \in [0, 1]$ for which
$$ x\left(p\right) < \frac{\int_0^p x\left(p'\right)dy\left(p'\right)}{y\left(p\right)}? $$
Thanks!