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Aug 13, 2020 at 1:04 comment added Math604 i did not look at that exact paper. My question is not very well posed since I really have a different example in mind. The above example the radial solution is decreasing in $r$ and then I know how to prove non-degeneracy. So even though my end goal is to prove nondegeneracy I am really more asking about this dependence on $t$ and smoothness in $t$.
Aug 12, 2020 at 15:09 comment added GabS Did you look at the paper of Zhang Liqun (Communications in PDE 1992) titled "Uniqueness Of Positive Solutions In A Ball". I believe there is a section on non-degereneracy.
Aug 7, 2020 at 23:28 history asked Math604 CC BY-SA 4.0