I too had a neighbor problem with a dog, two actually. After several 'talks' I put the word out that dogs on my property messing with any of my animals would be shot. I did check with my ordinances and I am completely within my rights to do that to protect my livestock from predators on my property. In my case that was all it took. He kept his dogs in a fenced yard from then on, I guess he believed me. Another option is to trap the dog yourself and turn it in to animal control. I have done that also. When they have to pay the fee to get their dog back that sometimes works also. Some people are very irresponsible and clueless. My preference is not to shoot the dog, it's just being a dog. It's 100% the owners fault. But you have to do what you have to do. I also have a donkey with my smaller livestock, and he will gladly dispatch a dog.