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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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