## 留言板

 引用本文: 林宗池, 林苏榕. 一类向量四阶非线性微分方程边值问题的奇摄动[J]. 应用数学和力学, 1988, 9(5): 385-395.
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.
 Citation: 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.

## Singular Perturbation of Boundary Value Problem for a Vector Fourth Order Nonlinear Differential Equation

• 摘要: 我们研究伴有边界摄动的向量边值问题:
ε2y(4)=f(x,y,y″,ε,μ)(μy(x,ε,μ)|x=μ=A1(ε,μ),y(x,ε,μ)|x=1-μ=B1(ε,μ)
y″(x,ε,μ)|x=μ=A2(ε,μ),y″(x,ε,μ)|x=1-μ=B2(ε,μ)
其中y,f,Aj和Bj(j=1,2)是n维向量函数和ε,μ是两个正的小参数.虽然纯量边值问题曾有人研究过,但这样的向量边值问题尚未被研究.在适当的假设下,利用微分不等式方法,我们找到向量边值问题的一个解和获得一致有效的渐近展开式.
•  [1] Howes, F.A., Differenual inequalities and applications to nonlinear singular perturbation problems, J. of Diff. Eqs., 20(1976), 133-149. [2] Chang, K.W. and F.A.Howes, Nonlinear Singular Perturbation Phenomena: Theory and Applications, Springer-Verlag. New York, Berlin, Heidelberg. Tokyo(1984). [3] O'Malley, R.E., Introduction to Singular Perturbations, Academic Press(1974). [4] 林宗池、郑永树,高阶常微分方程边值问题的奇摄动(I),福建师大学报(自然科学版), 2(1980),13-28. [5] 刘光旭,关于奇摄动拟线性系统,应用数学和力学,8,11 (1987), 967-976. [6] Kelley, W.G., A geometric method of studying two point boundary value problems for second order systems, Rocky Moun. J. of Math., 7(1977), 251-263. [7] Kelley, W.G., Boundary value problems for pairs of second order equations containing a small parameter, Rocky Moun. J. Math., 12, 4(1982), 655-667.

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##### 出版历程
• 收稿日期:  1987-02-20
• 刊出日期:  1988-05-15

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