Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/120191


Title: On the positive solutions of the differential equation $u''-u^p=0$.
Authors: 李明融
Li, Meng-Rong
Contributors: 應數系
Date: 2004
Issue Date: 2018-09-28 16:20:11 (UTC+8)
Abstract: 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.
Relation: Bulletin of the Institute of Mathematics. Academia Sinica (Bull. Inst. Math. Acad. Sinica), Vol. 32 No. 3, 145-172
AMS MathSciNet:MR2095180
Data Type: article
Appears in Collections:[應用數學系] 期刊論文

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