關於非線性微分方程的正則性

Abstract

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.

Introduction.\r\nChapter 0 The Calligraphy Equation.\r\nChapter I The Equation u``-u^p=0, p belogns to positive integer.\r\nChapter II The Equation u``-u^p=0, p belongs to rational number.\r\nChapter III The Blow-up Rate and Blow-up Constant.\r\nAppendix Proof of Theorem 5.