I have asked this question at MSE but got no response. I have rephrased it so that anyone who knows operator theory and integral equations could help me out... I faced a problem in physics which is a non-linear Fredholm integral equation (Hammerstein). It is of the form: \begin{equation} y(p)=f(p)+\int_0 ^{\infty}\frac{e^{ik∧p}}{y(k)}dk \end{equation} There are two subtleties:
- The kernel is non-degenerate or non-separable.
- The non-linearity is reciprocal.
The kernel is symmetric as the wedge product is anti-symmetric,i.e. $\overline{K(p,k)}=K(k,p)$. I tried solving it using the collocation method but got divergence due to it's severe bound on the upper limit. I am now starting to work with Monte-Carlo integration and it's too complicated. That's why I want to know if any of you could help me.