• Chỉ mục bởi
  • Năm xuất bản

Exhaustive existence and non-existence results for Hardy–Hénon equations in Rn

Giga Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan|
Quốc Anh (9435512400) | Yoshikazu (7003326857); Ngô University of Science, Vietnam National University, Hanoi, Viet Nam|

Partial Differential Equations and Applications Số 6, năm 2022 (Tập 3, trang -)

ISSN: 26622963

ISSN: 26622963

DOI: 10.1007/s42985-022-00190-3

Tài liệu thuộc danh mục:



Tóm tắt tiếng anh
This paper concerns solutions to the Hardy–Hénon equation -Δu=|x|σupin 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. © 2022, The Author(s).

Xem chi tiết