This sounds like a case of trespass , ( because of the disposal) and start by talking to the neighbor's and bring photographs.
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If they are being dropped in the same general area, setting up a motion activated wildlife camera (no pun intended) might be useful for obtaining proof of who is responsible. It may or may not be the person you think is the most obvious choice.
I love Mr. Pate's suggestion to catch them red-handed.
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