What can do about these cats?

How can we get rid of all cats in the apartment complex that are feral or stray or making a gosh-dang mess of the whole apartment complex? big apartment complex. Tried contacting animal department and animal shelters. they come and they leave a note, "Could not find any animals". Called them again, they come when I'm away, they leave a note, "Could not find any animals". Calling them again, same old thing, they arrive, they can't find any cats, they leave a message, "Couldn't find any animals". OK, so forget them. Is there a way we can get rid of all of them, so we don't have noisy, disease-infested, nuisances, ugly, broken-toilet cats running around in our neighborhood? I know what **I** would do, but some people might not like it. What should we do?