An interface problem with singular perturbation on a subinterval

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• 作者：Feng Xie (1)
  
  1. Department of Applied Mathematics ; Donghua University ; Shanghai ; 201620 ; P.R. China
  
• 关键词：34E10 ; 34A36 ; 34B15 ; lower and upper solutions ; singular perturbation ; interface conditions
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,088 KB
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  10. O鈥橫alley, RE (1991) Singular Perturbation Methods for Ordinary Differential Equations. Springer, New York CrossRef
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• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper we investigate an interface problem with singular perturbation on a subinterval. We first establish a lemma of lower and upper solutions which is an extension of the classical theory of lower and upper solutions. Based on the basic lemma we obtain the existence of a solution to the proposed problem, and the asymptotic behavior of solution as the singular perturbation parameter \(\varepsilon\rightarrow 0^{+}\) as well.