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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (2): 180-184    DOI:
    
A class of singularly perturbed boundary value problems for fourth order differential equations
XU You-wei, YAO Jing-sun
College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, China
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Abstract  Using the method of composite expansion and the theory of differential inequality, a class of singularly perturbed boundary value problems for fourth order equations are studied. The formal asymptotic solutions of the problems are constructed by the method of composite expansion. Then the existence of solutions for the original problems and the uniform validity of the formal asymptotic solutions are proved by the theory of differential inequality. At last, an example is given to illustrate the significance of the obtained result.

Key words： singular perturbation      boundary value problem      one-sided Nagumo condition      the theory of differential inequality     
Received: 22 September 2013      Published: 28 July 2018
CLC:  O175.14  
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XU You-wei
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Cite this article:

XU You-wei, YAO Jing-sun. A class of singularly perturbed boundary value problems for fourth order differential equations. Applied Mathematics A Journal of Chinese Universities, 2014, 29(2): 180-184.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I2/180


一类四阶微分方程的奇摄动边值问题

运用合成展开法和微分不等式理论研究了一类四阶方程的奇摄动边值问题. 先运用合成展开法, 构造了问题的形式渐近解, 再运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性. 最后用一个例子来说明所得结果的意义.

关键词： 奇摄动,  边值问题,  单边Nagumo条件,  微分不等式理论 
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