Timeline for How many non-trivial solutions can a semilinear elliptic equation have on a smooth star-shaped bounded domain with 0-Dirichlet boundary conditions?
Current License: CC BY-SA 4.0
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| Sep 16 at 16:28 | answer | added | Denis Serre | timeline score: 1 | |
| Sep 16 at 11:52 | comment | added | monotone operator | Thank you Professor.@DenisSerre. There are many papers on this topic, but these are too advanced for me. But unfortunately, I'm not familiar with 70s' papers concerning this. I know that the situation is very complex and the complexity depends on the geometry of the domain(so I constrain it to star-shaped), the nonlinearity(so I consider the above special type concerning parameter $\lambda$) | |
| Sep 16 at 11:43 | comment | added | Denis Serre | This topic was fashionable in the 70s. An early paper (J. Leray ?) studied such an equation in the sphere. Depending upon the space dimension, there could exist infinitely many radial solutions. | |
| Sep 16 at 11:14 | history | edited | monotone operator | CC BY-SA 4.0 |
added 18 characters in body
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| Sep 16 at 11:09 | history | asked | monotone operator | CC BY-SA 4.0 |