|
|
- 2015
一个奇摄动四阶微分方程的非线性混合边值问题
|
Abstract:
摘要： 研究了一个带非线性混合边界条件的四阶非线性微分方程的奇摄动边值问题。运用合成展开法构造了该问题的形式渐近解, 并利用微分不等式理论证明了该问题解的存在性, 给出了渐近解关于精确解的误差估计。
Abstract: A singularly perturbed boundary value problem for forth-order nonlinear differential equation with nonlinear mixed boundary condition is studied. The formal asymptotic solution is constructed by using the composite expansion method. According to the theory of differential inequalities, the existence of solution for the problem is proved and the error estimate of asymptotic solution is given
| [1] | 吴有萍, 姚静荪, 庄红艳. 一类具非线性边值条件的双参数奇摄动问题[J]. 高校应用数学学报, 2011, 26(3):288-294. WU Youping, YAO Jingsun, ZHUANG Hongyan. A class of singularly perturbed problem with two parameters and nonlinear boundary value conditions[J]. Applied Mathematics A Journal of Chinese Universities, 2011, 26(3):288-294. |
| [2] | 刘燕, 姚静荪. 一类高阶方程的非线性边界条件的奇摄动问题[J]. 高校应用数学学报, 2012, 27(2):175-181. LIU Yan, YAO Jingsun. A class of singular perturbed problems with nonlinear boundary value conditions for higher order equations[J]. Applied Mathematics A Journal of Chinese Universities, 2012, 27(2):175-181. |
| [3] | MO Jiaqi, LIU Shude. A class of nonlinear singularly perturbed problems of fourth order[J]. Chinese Quarterly Journal of Mathematics, 1997, 12(1):35-37. |
| [4] | YAO Jingsun. Asymptotic solution of the three points boundary value problem for nonlinear third-order equation[J]. Mathematica Applicata, 2009, 22(2):437-442. |
| [5] | 莫嘉琪. 四阶非线性微分方程边值问题的奇摄动[J]. 安徽师范大学学报: 自然科学版, 1987(01):110. MO Jiaqi. Singular perturbation of boundary value problems for fourth order nonlinear differential equations[J]. Journal of Anhui Normal University: Natural Science, 1987(01):110. |
| [6] | 王秀群, 倪守平. 四阶微分方程三点边值问题的奇摄动[J]. 数学物理学报, 2002, 22A(1):41-47. WANG Xiuqun, NI Shouping. Singular perturbation of three-pointed boundary value problems for fourth order differential equations[J]. ACTA Mathematica Scientia, 2002, 22A(1):41-47. |
| [7] | OMALLEY R E. Introduction to singular perturbations[M]. New York: Academic Press, 1974. |
| [8] | 占小丽, 余赞平, 周哲彦. 两类带非线性混合边界条件的四阶微分方程三点边值问题[J]. 福建师范大学学报: 自然科学版, 2013, 29(1):15-19. ZHAN Xiaoli, YU Zanping, ZHOU Zheyan. Two classes of three-point boundary value problems for forth-order differential equations with nonlinear and boundary conditions[J]. Journal of Fujian Normal University: Natural Science, 2013, 29(1):15-19. |
