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.


  • $\begingroup$ I doubt much can be done when you have the "current" value of $f$ dependent on "future" values. $\endgroup$ – Ian Jun 6 '16 at 23:29
  • $\begingroup$ What support can we expect these functions to have? $\endgroup$ – mathreadler Jun 7 '16 at 9:13
  • $\begingroup$ 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. $\endgroup$ – mathreadler Jun 7 '16 at 9:52

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