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Dec 17, 2021 at 9:37 comment added Math604 thanks for the answer. I think i managed to do something similar. I had worked with the $C(x)$ term and then worked an a slightly bigger domain with $ \phi$ the first eigenfunction on the larger domain (whose first eigenfunction is slightly smaller than $ \mu$). This gives me something; but for applications i would need the original claimed statement. So just to be clear; do you agree that it appears the result is false? For the case of general $C(x)$ i think I can easily come up with counterexamples (but maybe for the nonlinear problem i can't)
Dec 17, 2021 at 7:42 history edited username CC BY-SA 4.0
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Dec 17, 2021 at 7:36 history answered username CC BY-SA 4.0