政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/110835

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/110835

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/110835

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/110835

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:	[Department of Mathematical Sciences] Theses

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