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Structure of the Positive Radial Solutions for the Supercritical Neumann Problem ε2Δu − u + up = 0 in a Ball
http://hdl.handle.net/2261/59552
http://hdl.handle.net/2261/59552c37d8fc5-ef51-4c89-a499-4a13a2c66055
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms220303.pdf (343.5 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2016-07-19 | |||||
| タイトル | ||||||
| タイトル | Structure of the Positive Radial Solutions for the Supercritical Neumann Problem ε2Δu − u + up = 0 in a Ball | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Global bifurcation diagram | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | intersection number | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | singular solution | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Joseph-Lundgren exponent | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Miyamoto, Yasuhito
× Miyamoto, Yasuhito |
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| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We are interested in the structure of the positive radial solutions of the supercritical Neumann problem in a unit ball ε2(U''+ N−1/r U) − U + Up = 0, 0 < r < 1, U'(1) = 0, U >0, 0 < r < 1, where N is the spatial dimension and p > pS := (N + 2)/(N − 2), N ≥ 3. We showthat there exists a sequence {ε∗n}∞n=1 (ε∗1 > ε∗2 > ···→0) such that this problem has infinitely many singular solutions {(ε∗n, U∗n)}∞n=1 ⊂ R×(C2(0, 1)∩C1(0, 1]) and that the nonconstant regular solutions consist of infinitely many smooth curves in the (ε,U(0))- plane. It is shown that each curve blows up at ε∗n and if pS < p < pJL, then each curve has infinitely many turning points around ε∗n. Here, pJL := 1 + 4/N−4−2√N−1 (N ≥ 11), ∞ (2 ≤ N ≤ 10). In particular, the problem has infinitely many solutions if ε ∈ {ε∗n}∞n=1. We also showthat there exists ¯ε > 0 such that the problem has no nonconstant regular solution if ε > ¯ε. The main technical tool is the intersection number between the regular and singular solutions. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 22, 号 3, p. 685-739, 発行日 2015-07-15 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR | ||||||
| Mathmatical Subject Classification | ||||||
| 35J25(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 25B32(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 34C23(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 34C10(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2013-12-04 | ||||||
