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Hokkaido University Preprint Series in Mathematics >
EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN Rn
| Title: | EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN Rn |
| Authors: | GIGA, YOSHIKAZU Browse this author | | NGO, QUOC ANH Browse this author |
| Issue Date: | 24-Jan-2022 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1143 |
| Start Page: | 1 |
| End Page: | 30 |
| Abstract: | This 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/83871 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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