## Optimization of the «multiintegral» functional

Good day!
The sense of the problem: there is the following functional
$J=\int_{x_1 }^{x_2 } {F\left( {\frac{b(x)}{\int {b(x)dx} }} \right)dx}$
$b(x)=\int {a\left( {x,y,q(x,y),\int {q(x,y)dx} )} \right)dy}$

*All " indefinite" integrals are in the infinite limits, ${x_1 }$, ${x_2}$ – some numbers, $a(..), F(..)$ - some known functions.
We need to find such function $q(x,y)$ that the functional $J$ will possess it’s minimum value.