If you want to "keep" the cats and have (or can build) a location they can enter to get their food, but want to keep the other neighborhood animals out, there are a number of "electronic" pet doors available like these:

http://www.moorepet-petdoors.com/Electronic-and-Automatic-Pet-Doors-s/24.htm

It is a pretty simple concept; the cats wear a magnetic collar that unlocks the pet door so only they will have access to the food in the controlled area.

Or you can do what we do: Food goes outside at night and gets brought inside the door during the day. Easy-cheesy.