We're stuck on the following question in a problem relevant to a physics paper on AdS/CFT that we are working on. Given a Fredholm equation of second kind with the form f+int_D K f dx = 0, where \int_D K fdx is not a contraction and D is compact, what are some of the general cases in which f=0 is the unique solution?

Alternatively, what restrictions on K does one have to put to obtain a unique solution?

Thanks, Ning