# Other half of Gronwall

I am looking to show that if y(t) is continuous on (a, b) and satisfies

$$y(t)\leq H+K\int_{t}^{t_{0}} y(s)ds,\quad\forall\ a

where $$t_0 \in (a,b)$$, then

$$y(t)\leq He^{K(t_0-t)},\quad\forall\ a

• Do you want $h(s)$ and not $y(s)$ under your integral sign? – Robert Lewis Oct 22 '18 at 22:55
• In this case what is the function $h$ ? – Delta-u Oct 23 '18 at 13:20
• That is a great question. Perhaps that is the trouble with it. Let's suppose that was a mistake. I will change the question to represent that. – Sekkou527 Oct 23 '18 at 15:07