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1	關於非線性微分方程的正則性 / The Regularity of Solutions for Non-linear Differential Equation u'' - u^p = 0 林俊宏, Lin, Jiunn-Hon Unknown Date (has links) 本研究中討論了非線性微分方程式之解的正則性。在這之中發現了一些有趣的現象，得到了方程式解可以做任意次的微分，並且得到對該解任意次微分後其值趨近到無限大時之爆破速率、爆破常數及當其值遞減至零時的爆破速率、爆破常數。 / In this paper we work with the regularity of solutions for the non-linear ordinary differential equation u''-u^p=0 for some well-defined functions u^p. We have found some interesting phenomena, u belongs to C^q for any q in positive integer, blow-up constant, blow-up rate, null point and decay rate of u^(n) are obtained in this work, through that we get the characterization for these equations in this case. 微分方程正則性爆破爆破速率 differential equation regularity blow-up blow-up rate