Consider the following Fredholm integral equation of the second kind $$ \phi(s) = \frac{s(1-s^2)}{(1+s^2)^4} + \lambda \int_0^1 \phi(t) \ln \left| \frac{s+t}{s-t} \right| \, \mathrm{d} t \, , \quad\quad (0<s<1) \, , $$ wherein $\lambda$ is a known quantity and $\phi(s)$ is the unknown function. I have tried to use the method of successive substitution but it turns out to be inconvenient for a logarithmic kernel function.

I was wondering whether other analytical approaches can be employed for this case. Any help is highly appreciated.




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