Singular Perturbation of boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on infinite Interval(Ⅰ)

Zhao Wei-li

Volume 10 Issue 1

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1989 > 10(1): 43-50

Zhao Wei-li. Singular Perturbation of boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on infinite Interval(Ⅰ)[J]. Applied Mathematics and Mechanics, 1989, 10(1): 43-50.

Citation:

PDF( 1885 KB)

Singular Perturbation of boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on infinite Interval(Ⅰ)

Zhao Wei-li

Department of Mathematics, Jilin University, Changchun

Received Date: 1986-09-20
Publish Date: 1989-01-15

Abstract

Abstract

In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameter are examined, where α_i, β are constants, and i=0,1.

FullText(HTML)

References(10)

References

[1]	伍卓群,一类常微分方程边值问题的奇摄动—(I)方程式的情形,吉林大学自然科学学报,2(1963),91-104.
[2]	周钦德,一类常微分方程奇摄动问题解的渐近展开,吉林大学自然科学学报,4 (1979),1-19.
[3]	周钦德,一类奇摄动边值问题解的渐近展开,吉林大学自然科学学报,4 (1980),12-26
[4]	周钦德,一类奇摄动边值问题近似常数解的渐近展开,吉林大学自然科学学报,2 (1981),12-22.
[5]	周钦德,某类奇摄动边值问题解的渐近展开,吉林大学自然科学学报,3 (1981),37-50.
[6]	赵为礼,一类常微分方程无穷边值问题的奇摄动,吉林大学自然科学学报,3 (1881),27-36.
[7]	Scbrader,K.W.,Existence theorems for second order boundary value problems,J.Diff.Eqs.,5(1969),572-584.
[8]	Nagumo.M.,Uber die Differentialgleichung y"=f(x,y,y'),Proc.Phys.Math.Soc.Japan.19 Ser 3,10(1937),861-866.
[9]	Jackson.L.K.,Subfunctions and second-order ordinary differential inequalities,Adv.Math.,2(1968),307-363.
[10]	Klaasen.G.A.,Differential inequalities and existence theorems for second and third order boundary value problems.J.Diff.Eqs.,10(1971),529-537.

Relative Articles

[1]	ZHU Hongbao, CHEN Songlin. A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1292-1296. doi: 10.21656/1000-0887.410082
[2]	FENG Yi-hu, MO Jia-qi. Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1405-1411. doi: 10.21656/1000-0887.380008
[3]	YAO Qing-liu. Solvability of a Class of Second-Order Quasilinear Boundary Value Problems[J]. Applied Mathematics and Mechanics, 2009, 30(8): 990-996. doi: 10.3879/j.issn.1000-0887.2009.08.012
[4]	LI Ming-zhong, XU Ding-hua. A Class of Nonlinear Boundary Value Problems for the Sceond-Order E₂ Class Elliptic Systems in General Form[J]. Applied Mathematics and Mechanics, 2003, 24(2): 146-162.
[5]	WANG Guo-can, JIN Li. Third Order Nonlinear Singularly Perturbed Boundary Value Problem[J]. Applied Mathematics and Mechanics, 2002, 23(6): 597-603.
[6]	LI Ren-gui, LIU Li-shan. Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(4): 435-440.
[7]	Chen Yusen. Singular Perturbation of Second Order Nonlinear System With Boundary Perturbation[J]. Applied Mathematics and Mechanics, 2000, 21(2): 201-208.
[8]	Zhou Yali, You Zhefeng, Lin Zongchi. Singular Perturbation of General Boundary Value Problem for Nonlinear Differential Equation System[J]. Applied Mathematics and Mechanics, 1998, 19(6): 497-504.
[9]	Huang Weizhang. Boundary Value Problem for a Singularly Perturbed Nonlinear System[J]. Applied Mathematics and Mechanics, 1997, 18(6): 535-544.
[10]	Chen Songlin. Singular Perturbation for a Nonlinear Boundary Value Problem of First Order System[J]. Applied Mathematics and Mechanics, 1996, 17(11): 1033-1038.
[11]	Lin Zong-chi, Lin Su-rong. Singular Perturbation of Initial Value Problem for a Nonlinear Second Order Systems[J]. Applied Mathematics and Mechanics, 1993, 14(2): 95-100.
[12]	He Qing, Ji Chun-ci. The Existence of Solution of a Class of Two-Order Quasilinear Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1992, 13(10): 941-944.
[13]	Kang Lian-cheng. On Singular Perturbation for a Nonlinear initial-Boundary Value Problem(Ⅱ)[J]. Applied Mathematics and Mechanics, 1992, 13(2): 135-143.
[14]	Zhao Wei-li. Singular Perturbation of Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations on Infinite Interval (Ⅱ)[J]. Applied Mathematics and Mechanics, 1991, 12(11): 1037-1048.
[15]	Lin Ping, Su Yu-cheng. Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points[J]. Applied Mathematics and Mechanics, 1989, 10(11): 955-959.
[16]	Lin Zong-chi, Lin Su-rong. Singular Perturbation of Boundary Value Problem for a Vector Fourth Order Nonlinear Differential Equation[J]. Applied Mathematics and Mechanics, 1988, 9(5): 385-395.
[17]	Xu Jun-tao. Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation[J]. Applied Mathematics and Mechanics, 1988, 9(7): 629-640.
[18]	Zhou Qin-de, Miao Shu-mei. Boundary Value Problems for Second Order Singularly Perturbed Differential Equations[J]. Applied Mathematics and Mechanics, 1988, 9(1): 91-94.
[19]	Liang Zhong-chao, Chen Shao-zhu. Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(11): 1027-1034.
[20]	K. W. Chang, Lin Zong-chi. Singular Perturbation of Nonlinear Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1984, 5(5): 603-612.