刘锡平,贾梅.具有分数导数的p-Laplace方程非局部边值问题的多个正解[J].数学研究及应用,2012,32(3):327~336
具有分数导数的p-Laplace方程非局部边值问题的多个正解
Multiple Positive Solutions of Nonlocal Boundary Value Problems for $p$-Laplacian Equations with Fractional Derivative
投稿时间:2010-11-19  最后修改时间:2011-04-18
DOI:10.3770/j.issn:2095-2651.2012.03.007
中文关键词:  p-Laplace微分方程  Caputo分数导数  积分边值问题  单减正解  Avery-Peterson不动点定理.
英文关键词:$p$-Laplacian differential equations  Caputo fractional derivative  integral boundary value problems  positive decreasing solutions  Avery-Peterson fixed point theorem.
基金项目:国家自然科学基金(Grant No.11171220), 上海市教委科研创新基金重点项目(Grant No.10ZZ93).
作者单位
刘锡平 上海理工大学理学院, 上海 200093 
贾梅 上海理工大学理学院, 上海 200093 
摘要点击次数: 1775
全文下载次数: 1927
中文摘要:
      本文研究了一类具有Caputo分数导数的p-Laplace微分方程积分边值问题的多个正解的存在性,应用 Avery-Peterson 不动点定理得到了非局部边值问题至少有三个单调递减的正解存在的结论.最后给出了应用实例,用于说明我们所得到的结论.
英文摘要:
      In this paper, we study the multiple positive solutions of integral boundary value problems for a class of $p$-Laplacian differential equations involving the Caputo fractional derivative. Using a fixed point theorem due to Avery and Peterson, we obtain the existence of at least three positive decreasing solutions of the nonlocal boundary value problems. We give an example to illustrate our results.
查看全文  查看/发表评论  下载PDF阅读器