Timeline for Non-existence of rapidly decaying solutions of certain elliptic semilinear equations
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2022 at 21:36 | comment | added | Willie Wong | For your comment: Suppose $- \Delta (u-v) + m(u-v) + \lambda (u^p - v^p) = 0$. Assuming you are looking at real valued functions: if $p$ is odd then $u\mapsto u^p$ is strictly increasing, and so $(u^p - v^p)(u-v) \geq 0$. Then the same argument tells you that $\|u-v\|_{L^2} = 0$. | |
| Mar 1, 2022 at 21:18 | comment | added | S.Z. | I wonder if a similar argument could show that the nonlinear operator on the left side of the equation is injective or one needs some global inverse function theorem for that? | |
| Mar 1, 2022 at 20:53 | vote | accept | S.Z. | ||
| Mar 1, 2022 at 19:20 | history | answered | Willie Wong | CC BY-SA 4.0 |