Neighbor's mean cat
My neighbor's cat comes over to our place and beats up on my cats, inflicting significant damage. Two trips to the vet for abscess drains has cost me $1400. Also, a stray wandered into our house a month ago with a large scratch wound on it's head and 2 abcesses from bites; another $650. I didn't see this attack so I can't blame the neighbor's cat but I did see the attacks on my 2 cats.
Any suggestions on how to stop this from happening, short of firing a shotgun in a populated area?
I have spoken with the neighbors and they deny owning their cat, saying yes, they feed it but "it's not really ours".
I have captured/cornered their cat in our garage twice and have shown it a pretty difficult time; once mashing it into a corner with a broom and soaking it with a bucket of water but he keeps coming back. My vet said some cats are just very agressive and territorial and it will never stop.