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Jan 28, 2020 at 16:56 comment added Math604 If I look for ground state solutions and let $ \mu_t$ denote the minimal energy iti appears I can show the energy is differentiable (well at least the quotients are bounded). So this is halfway to showing the solution is differentiable in $t$ I guess I should delete the question for now.
Jan 27, 2020 at 23:08 history asked Math604 CC BY-SA 4.0