2023-09-24T05:13:18Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/838712022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN RnGIGA, YOSHIKAZUNGO, QUOC ANHopen access410This paper concerns solutions to the Hardy–Hénon equation −Δu = |x|σup in Rⁿ with n ≥ 1 and arbitrary p, σ ∈ R. This equation was proposed by Hénon in 1973 as a model to study rotating stellar systems in astrophysics. Although there have been many works devoting to the study of the above equation, at least one of the following three assumptions p > 1, σ ≥ −2, and n ≥ 3 is often assumed. The aim of this paper is to investigate the equation in other cases of these parameters, leading to a complete picture of the existence/non-existence results for non-trivial, non-negative solutions in the full generality of the parameters. In addition to the existence/non-existence results, the uniqueness of solutions is also discussed.Department of Mathematics, Hokkaido University2022-01-24engdepartmental bulletin paperVoRhttps://doi.org/10.14943/100919http://hdl.handle.net/2115/8387110.14943/100919Hokkaido University Preprint Series in Mathematics1143130https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/83871/1/ExhExiNon.pdfapplication/pdf580.72 KB2022-01-24