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具有不连续系数的三阶半线性奇异摄动边值问题

薛虎 谢峰

薛虎, 谢峰. 具有不连续系数的三阶半线性奇异摄动边值问题[J]. 华东师范大学学报(自然科学版), 2017, (2): 20-28. doi: 10.3969/j.issn.1000-5641.2017.02.003
引用本文: 薛虎, 谢峰. 具有不连续系数的三阶半线性奇异摄动边值问题[J]. 华东师范大学学报(自然科学版), 2017, (2): 20-28. doi: 10.3969/j.issn.1000-5641.2017.02.003
XUE Hu, XIE Feng. Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients[J]. Journal of East China Normal University (Natural Sciences), 2017, (2): 20-28. doi: 10.3969/j.issn.1000-5641.2017.02.003
Citation: XUE Hu, XIE Feng. Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients[J]. Journal of East China Normal University (Natural Sciences), 2017, (2): 20-28. doi: 10.3969/j.issn.1000-5641.2017.02.003

具有不连续系数的三阶半线性奇异摄动边值问题

doi: 10.3969/j.issn.1000-5641.2017.02.003
基金项目: 

上海市自然科学基金 15ZR1400800

详细信息
    作者简介:

    薛虎, 男, 硕士研究生, 研究方向为奇异摄动理论.E-mail:13918501496@163.com

    通讯作者:

    谢峰, 男, 教授, 研究方向为奇异摄动理论及其应用.E-mail:fxie@dhu.edu.cn

  • 中图分类号: O175.14

Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients

  • 摘要: 主要研究了一类具有不连续系数的奇异摄动边值问题解的存在性和渐近估计.首先,利用Schauder不动点定理,建立一般问题的上下解定理;其次,利用边界函数法,构造出形式渐近解,并基于已确立的上下解定理,证明解的存在性和一致有效性;最后给出实例验证主要结论.
  • [1] 周明儒, 林武忠, 倪明康, 等.奇异摄动导论[M].北京:科学出版社, 2014.
    [2] 周明儒, 杜增吉, 王广瓦.奇异摄动中的微分不等式理论[M].北京:科学出版社, 2012.
    [3] 倪明康, 林武忠.奇异摄动中的渐近理论[M].北京:科学出版社, 2009.
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    [16] 丁海云, 倪明康.具有不连续源的奇异摄动边值问题[J].数学杂志, 2012, 32(6):1121-1128. http://www.cnki.com.cn/Article/CJFDTOTAL-YONG201304013.htm
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出版历程
  • 收稿日期:  2016-01-06
  • 刊出日期:  2017-03-25

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