Homogeneous Fredholm equation of the second kind

Hi,

during the analysis of a problem in my phd thesis

I have resulted in the following equation.

which is clearly a *homogeneous Fredholm equation of the second kind*

The problem is that I can't find in any text any way of solving it.

Solutions are provided only for special cases like when the kernel K

is symmetric

or when it is separable which are both not my case.

The particular form of the equation I am dealing with is

where is symmetric and depends only in the difference x-t, , and g(x) a known function involving logarithm.

Any ideas of how to deal with this kind of form?

Thank you in advance