In signal processing theory, I found this integral equation which I suppose to be of Hammerstein type: $$u(t)-\int_0^1\frac{\cos(\omega t+\phi)}{u(\phi)}d\phi=0$$ I didn't find anything in literature apart this:
http://www-users.mat.uni.torun.pl/~tmna/files/v15n2-02.pdf
Could someone give me some hints how to solve this equation? Thanks.