EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN Rn

GIGA, YOSHIKAZU; NGO, QUOC ANH

Hokkaido University Preprint Series in Mathematics, 2022, 1143, 1-30

Permalink : https://doi.org/10.14943/100919

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アクセス権	open access
DOI	https://doi.org/10.14943/100919
URI	https://hdl.handle.net/2115/83871
タイトル	EXHAUSTIVE EXISTENCE AND NON-EXISTENCE RESULTS FOR HARDY–HÉNON EQUATIONS IN Rn
著者	著者名 GIGA, YOSHIKAZU
著者	著者名 NGO, QUOC ANH
言語	英語
発行日	2022-01-24
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1143
ページ	1-30
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record