Solve A(x) ∆F[f]/∆f + J(x)F[f] = 0

[Karlisbad]

Differential equation??

Let be F a functional of f(x) and J(x) and A(x) a function, then can we solve this?:

$$A(x)\frac{\delta F[f]}{\delta f}+J(x)F[f]=0$$

J and A are known functions and F[f] is an unknown functional satisfying the equation above.

 

[CPL.Luke]

does f have to depend on x?

 

[CPL.Luke]

and are you sure you don't mean F(x)? becaue then all you need to do is substitute in a series solution.

 

[Karlisbad]

F is a functional (a function of function ) you introduce any function f(x) inside F and you get a number.. if F were a function i would know how to solve it...