Is it possible to obtain the functional derivative of the following functional?
$Z[q]=\int_0^T\int_0^t\int_0^t q(t'')K(t''-t')q(t')dt''dt'dt.$
I tried to apply the usual functional derivative definition (like here):
$\delta Z=\frac{\delta Z}{\delta q}= \frac{d}{d\epsilon}[\int_0^T\int_0^t\int_0^t (q(t'')+\epsilon \phi(t''))K(t''-t')(q(t')+\epsilon\phi(t'))dt''dt'dt]_{\epsilon=0}$
$\frac{\delta Z}{\delta q}= \int_0^T\int_0^t\int_0^t \phi(t'')K(t''-t')q(t') + q(t'')K(t''-t')\phi(t') dt''dt'dt$
But I can't see the end. Someone can help me?
Thanks!