關於非線性微分方程的正則性

• Main Authors: 林俊宏, Lin, Jiunn-Hon
• Language: 英文
• Published: 國立政治大學
• Subjects: 微分方程; 正則性; 爆破; 爆破速率; differential equation; regularity; blow-up; blow-up rate
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002001689%22.

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.