簡易檢索 / 詳目顯示
| 研究生： |
陳盈潤 |
|---|---|
| 論文名稱： |
二階非線性微分方程解的行為 On the behavior of solution for non-linear differential equation |
| 指導教授： | 李明融 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 中文 |
| 論文頁數： | 18 |
| 中文關鍵詞： | 解的爆炸時間 、解的最大存在時間 、Emden-Fowler方程式 |
| 外文關鍵詞： | Blow up time for solution, The lift-span for solution, Emden-Fowler equation |
| 相關次數： | 點閱：31 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在這篇論文,我們考慮半線性微分方程式的初始邊界值問題之解u,的存在性,唯一性,和他的行為.
(i) t^{-sigma}u''(t)=r_1u(t)^p+r_2u(t)^p(u'(t))^2, u(1)=u_0,u'(1)=u_1,
其中 p>1 為常數.
對t≥1,sigma>0,p>1 為偶數,r_1>0,r_2>0,u_0>0,u_1>0.
我們得到以下的結果.
1 Introduction 1
2 Fundamental lemma 4
2.1 Fundamental lemma 4
3 Some Solution Representations 7
3.1 Representation for v_s 7
3.2 Representation for v 8
4 Main Result 10
4.1 Estimate for v under unboundedness of the equation(2.1.3) when sigma>0, p>1 is even 10
5 Conclusion 16
Bibliography 17
[1]Meng-Rong Li On the Emden-Fowler equation u''-|u|^{p-1}u=0 Nonlinear Analysis 2006 vol.64 pp.1025-1056
[2]Meng-Rong Li.BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u''= |u|^{p} Acta Math.Sci., 2007 vol.4 pp.703-734
[3]Meng-Rong Li. ON THE EMDEN-FOWLER EQUATION u''(t)u(t)=c_1+c_2(u'(t))^2 when c_1≥0, c_2≥0 Acta Math.Sci., 2010 vol.30 4 pp.1227-1234
[4]Meng-Rong Li.ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF THE NONLINEAR DIFFERENTIAL EQUATION t^2u" = u^nElectronic Journal of Differential Equations,2013 vol.2013 No.250 pp.1-9.
[5]Meng-Rong Li. NONEXISTENCE OF GLOBAL SOLUTIONS OF EMDEN-FLOWER TYPE SEMILINEAR WAVE EQUATIONS WITH NON-POSITIVE ENERGY Electronic Journal of Differential Equations, 2016 vol.2016 No.93 pp.1-10.
[6]Meng-Rong Li. BLOW-UP SOLUTIONS TO THE NONLINEAR SECOND ORDER DIFFERENTIAL EQUATION u''(t)=u(t)^p(c_1+c_2u'(t)^q) (I) Acta Math.Sci., June 2008 vol.12 3 pp.599-621
[7]Meng-Rong Li and Yueloong Chang.A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION FOR SOME ENTERPRISES Acta Math.Sci.,2015 vol.35 5 pp.1014-1022
[8]Meng-Rong Li and Pai Jente. QUENCHING PROBLEM IN SOME SEMILINEAR WAVE EQUATIONS Acta Math.Sci., 2008 vol.28 3 pp.523-529
[9]Meng-Rong Li and Tzong-Hann Shieh. Numeric treatment of contact discontinuity with multi-gases Journal of Computational and Applied Mathematics 2009 vol.2009 pp.656–673
[10]Corey-Stevenson Powell. J.HOMER LANE AND THE INTERNAL STRUCTURE OF THE SUN JHA 1988 xix
此全文未授權公開