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| Title: | 二階非線性微分方程解的行為
On the behavior of solution for non-linear differential equation |
| Authors: | 陳盈潤 |
| Contributors: | 李明融
陳盈潤 |
| Keywords: | 解的爆炸時間
解的最大存在時間
Emden-Fowler方程式
Blow up time for solution
The lift-span for solution
Emden-Fowler equation |
| Date: | 2017 |
| Issue Date: | 2017-07-11 11:56:03 (UTC+8) |
| Abstract: | 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 |
| Reference: | [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 |
| Description: | 碩士
國立政治大學
應用數學系
102751015 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1027510151 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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