# Equation in integral form

I've been working with this equation where the unknown factor is the function $$f$$ that can be complex:

$$1 = f(\vec{x})\int_{\mathbb{R}^3}\ d^3y\ \frac{f(\vec{y})}{|\vec{x} - \vec{y}|^4}$$

Is there any way to solve this equation without using the trial-error method, i.e., without testing different forms for $$f$$? Anyway, can you see any solution?

• Is there not a problem with the integral when $y=x$? – user121049 Nov 1 '18 at 19:06
• Forget solving for $f$, I don't see how you choose a $f$ so that the integral is finite for any $x$, but maybe that's my lack of vision. – user121049 Nov 1 '18 at 20:02
• How do we deal with the singularity at $y=x$? – Yuriy S Nov 1 '18 at 20:07
• Well, from the point of view of the integral $x$ is just a parameter, so for integration I think you can suppose $x \neq y$ – Vicky Nov 1 '18 at 20:28