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Sep 20, 2014 at 4:30 comment added Craig @Christian. Sorry, for the wording. It definitly was not clear what i was asking.
Sep 20, 2014 at 3:27 comment added Christian Remling @Craig: Thanks for the clarification. I'll delete my answer, which seems pointless now.
Sep 20, 2014 at 1:08 comment added Craig @Christian and Connor. Yes my intended question was a Liouville theorem in the sense that I wanted a non-existence result, which appears not to be true by your examples. Thank you very much for the examples.
Sep 19, 2014 at 23:04 history edited Connor Mooney CC BY-SA 3.0
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Sep 19, 2014 at 23:02 comment added Connor Mooney @ChristianRemling: Yes, I interpreted the question as: Does the decay property of C always imply that decaying $u$ are trivial? Of course you are right that it seems to be true for most C.
Sep 19, 2014 at 19:54 comment added Christian Remling Actually, the OP mentions "Liouville type theorem" in the title, so maybe you are answering the intended question and I'm not. I guess we'll find out eventually...
Sep 19, 2014 at 15:49 history answered Connor Mooney CC BY-SA 3.0