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https://ah.lib.nccu.edu.tw/handle/140.119/120191
題名: | On the positive solutions of the differential equation $u``-u^p=0$. | 作者: | 李明融 Li, Meng-Rong |
貢獻者: | 應數系 | 日期: | 2004 | 上傳時間: | 28-Sep-2018 | 摘要: | The author studies the initial value problem for a second order nonlinear ordinary differential equation of the form u ′′ −u p =0 with p∈(0,1) and p∈(1,∞) . The author discusses the existence, blow-up of solutions and an estimate of their life span. This paper tries to cover a particular case of previous studies, namely what the author calls "the lower dimensional case of the semilinear wave equation``. The analysis is standard and it mainly uses energy estimates to analyse the behaviour of solutions of the above "conservative`` system. In this paper we work with the ordinary equation u ′′ −u p = 0 and obtain some interesting phenomena concerning blow-up, blow-up rate, life-span, zeros, critical points and the asymptotic behavior at infinity of solutions to this equation. |
關聯: | Bulletin of the Institute of Mathematics. Academia Sinica (Bull. Inst. Math. Acad. Sinica), Vol. 32 No. 3, 145-172 AMS MathSciNet:MR2095180 |
資料類型: | article |
Appears in Collections: | 期刊論文 |
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