Help! How do I keep dogs away from lawn?

In the past 6 months, it has been decided that the southeast corner of my lawn is a neighborhood restroom area for any dogs going by. This area is quite large and I've been noticing a lot more people walking their dogs in our neighborhood that aren't from our neighborhood. Of course, the humans aren't carrying any bags with them that I can see and from the evidence left behind, they're either not carrying the bags or not using them.

The area, like I said, is very large. Our backyard is fenced in but not all the way to the street. So not only are people letting their dogs defecate along our fence but also right in our front yard, where it isn't fenced in. Our own dog goes barking mad when the other dogs trespass on our property yet I still haven't been able to catch anyone "in the act".

One day, I did discover a woman with an extremely large german shepherd at our backyard gate. She was letting her dog stick it's face into the crack of our gate. My own dog was going insane, barking like crazy and growling. I don't know what was wrong with this woman, because she continued to just stand there at my fence and let her dog stick it's nose into the space. I told her the gate didn't work properly and that while we had piled up pieces of plywood and a lawn chair in front of the gate, I couldn't guarantee that my dog wouldn't get out. I then told her she needed to stay off of our property. The entire time I'm telling her this, she's just smiling away, saying "yeah" "ok" really slowly. I could see that she didn't have much control over her dog but that's no excuse to trespass on someone's property and purposely agitate another person's dog. I went in the house while she was still standing at the gate and she traveled to our front yard and let her dog defecate in our yard. I didn't discover this until a little while later. Nice, huh?

I checked our local hardware store and they do sell something to spread onto your lawn to discourage dogs but it's expensive and it's a small bottle for the area I need. Also I would need to reapply at least twice a week. I can't afford this

I just can't believe that so many people feel it's perfectly ok to come onto my property and let their dogs defecate right there in my yard and then they just walk away. It makes me even madder that these people aren't even from our neighborhood. I've seen them walk by with their dogs, so I know they aren't.

Does anyone know an inexpensive way to discourage dogs from using my yard as their bathroom? I thought about maybe placing a sign up that says the lawn has been chemically treated and is harmful to pets? Please help!