I've gotten two 30 day nuisance permits from IDNR and shot two of them. There are so many around here.I didn’t see from earlier responses but here in Georgia, bobcats can be hunted and killed, but only during regulated seasons. However, Georgia Dept of Natural Resources will usually give a kill or trap permit if requested in a case like yours. The last permit I got was for foxes and it was gods for 30 days and it was unlimited with respect to numbers. Just be sure that if you are going to take action, you aren’t looking at any legal issues with state.
With that said, if one is attacking my chickens, dogs or anything else, I will sort any issues out with law enforcement later.