# Kind of Gronwall Inequality

Does somebody knows if it is possible to obtain an inequality (like for Gronwall inequality) on $f$ if $f$ verify $$f(t) \leq A+\int_0^{2t} g(s)f(s) ds$$. Where $f$ and $g$ are as smooth as necessary and nonnegative.

Thanks.

• I doubt much can be done when you have the "current" value of $f$ dependent on "future" values. – Ian Jun 6 '16 at 23:29
• What support can we expect these functions to have? – mathreadler Jun 7 '16 at 9:13
• The integral is a correllation over a symmetric interval around $t$. Maybe you can rewrite it as a convolution and $f(t)$ as a dirac impulse convolution. – mathreadler Jun 7 '16 at 9:52