I have asked this question but got no response. I rephrase it so that anyone who knows operator theory and integral equations would 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\wedge p}}{y(k)}dk \end{equation} There are two subtleties: (1)The kernel is non-degenerate or non-separable.(2) 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 if any of you would help me.
2026-03-27 15:36:07.1774625767
Solution of non-linear Fredholm(Hammerstein) equation with non-degenerate kernel and reciprocal non-linearity
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