The equation is
$f(p) = \int_{0}^{\Lambda} dk \; \mathcal{M}(k,p;E) \, f(k)$,
where the kernel $\mathcal{M}$ is
$\mathcal{M}(k,p;E) = \frac{2/ m\pi}{1 - \sqrt{E + 3p^2/4}} \frac{k}{p} \log\left( \frac{E + k^2 + p^2 + kp}{E + k^2 + p^2 - kp}\right)$.
The parameter $E > 1$, and $\Lambda \gg 1$ is some cutoff coming from the underlying quantum field theory.
(For those in the know, this the homogeneous Skorniakov-Ter-Martirosyan equation for quantum three-particle bound states, projected to the s-wave chennel.)
Anyway, I don't even need to solve it. All I want to know is, for a given parameter E, if the equation admits a solution $f(p) \neq 0$.
This is my unenlightened way of thinking. Recast the equation into
$0 = \int dk \, [\mathcal{M} - \delta(p-k)] f(k),$
discretize the integral:
$0 = \sum_{k} G_{p,k} f_k$,
and see if and when $\det \lvert G \rvert$ goes to zero. I'm not even sure if it's working, because I haven't seen any zero so far!
Any comment and suggestion will be much appreciated. Please lend a helping hand to this numerically illiterate physicist!