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.
Bulletin of the Institute of Mathematics. Academia Sinica (Bull. Inst. Math. Acad. Sinica), Vol. 32 No. 3, 145-172 AMS MathSciNet:MR2095180