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We showthat there exists a sequence {ε∗n}∞n=1 (ε∗1 \u003e ε∗2 \u003e ···→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 \u003c p \u003c 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 \u003e 0 such that the problem has no nonconstant regular solution if ε \u003e ¯ε. 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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 |
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jms220303.pdf (343.5 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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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 | Global bifurcation diagram | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | intersection number | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | singular solution | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | Joseph-Lundgren exponent | |||||
主題Scheme | Other | |||||
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 | 415 | |||||
主題Scheme | NDC | |||||
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 |