Timeline for Non-uniqueness of solutions to a simple nonlinear elliptic PDE in $\mathbb R^n$

12 events

when toggle format	what		by	license	comment
S Oct 2, 2023 at 13:33	history	suggested	Ali Taghavi		a tag is added
Oct 2, 2023 at 13:26	review	Suggested edits
S Oct 2, 2023 at 13:33
Oct 1, 2023 at 19:43	comment	added	Lorenzo Pompili		Thank you for the comment! In that case you should be able to use the fixed point theorem to have existence and uniqueness of small solution for small $f\in L^2(\mathbb R^3)$, although the smallness assumption would in general depend on $\lambda$. I don’t know if it can be relaxed to well posedness for large data, or for well posedness uniform in $\lambda$
Oct 1, 2023 at 18:32	comment	added	Giorgio Metafune		Would the situation change if you consider $\lambda-\Delta$, $\lambda >0$, instead of $-\Delta$?
Oct 1, 2023 at 18:19	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 272 characters in body; edited title
Oct 1, 2023 at 18:14	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 272 characters in body; edited title
Oct 1, 2023 at 18:05	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 272 characters in body; edited title
Sep 30, 2023 at 12:18	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 162 characters in body
Sep 29, 2023 at 21:01	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 228 characters in body; edited title
Sep 29, 2023 at 20:55	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 228 characters in body; edited title
Sep 28, 2023 at 14:44	history	edited	Lorenzo Pompili	CC BY-SA 4.0	added 119 characters in body; edited title
Sep 28, 2023 at 14:37	history	asked	Lorenzo Pompili	CC BY-SA 4.0