{"id":"openai-math/The-Subcritical-Henon-Lane-Emden-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Subcritical-Henon-Lane-Emden-Conjecture-September-24-2026","tags":["pde","elliptic-equations","nonlinear-analysis"],"score":0,"title":"The Subcritical Hénon–Lane–Emden Conjecture","domain":"Partial differential equations","family":"370","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We prove the subcritical Hénon–Lane–Emden conjecture: for every dimension n ≥ 2, positive powers p , q , and real weights A , B , the system has no strictly positive entire solution when $`(n+A)/(p+1)+(n+B)/(q+1)\\gt n-2`$. Solutions need only be continuous at the origin and classical elsewhere, without a condition at infinity. For n ≥ 3 and $`A,B\\gt -2`$, combining this result with the radial existence theorem of Bidaut-Véron and Giacomini proves Phan's Conjecture C in full: a positive radial entire solution exists whenever the strict inequality fails.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"The Lane–Emden and Hénon–Lane–Emden conjectures"}