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具p-Laplace算子的四阶三点边值问题的两个正解 被引量：6

Two Positive Solutions for Fourth-Order Three-Point p-Laplacian Boundary Value Problems
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摘要 研究下列具有p-Laplace算子的四阶三点边值问题(p(u″(t)))″+a(t)f(u(t))=0,t∈(0,1),u(0)=ξu(1),u′(1)=ηu′(0),(p(u″(0))′=α1(p(u″(δ))′,p(u″(1))=β1(p(u″(δ)),通过利用Avery-Henderson不动点定理,给出了边值问题存在至少两个正解的充分条件. We study the following fourth-order three-point boundary value problem with p - Laplacian {（φp（u″（t）））″＋a（t）f（u（t））=0,t∈（0,1）,u（0）=ξu（1）,u′（1）=ηu′（0）,（φp（u″（0））′=α1（φp（u″（δ））′,φp（u″（1））=β1（φp（u″（δ））,By means of the fixed point theorem due to Avery and Henderson, Some sufficient conditions are obtained that guarantee the existence ofat least two positive solutions to the above boundary value problem.
作者 封汉颍 葛渭高
机构地区 北京理工大学数学系
出处 《数学的实践与认识》 CSCD 北大核心 2007年第24期140-146,共7页 Mathematics in Practice and Theory
基金 国家自然科学基金资助项目(10671012) 教育部博士点专项基金资助项目(20050007011)
关键词 边值问题 锥 不动点定理 正解 boundary value problem cone fixed point theorem positive solution
分类号 O175.8 [理学—基础数学]
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参考文献17

  • 1Agarwal R P, Regan D O, Wong P J Y. Positive Solutions of Differential [M]. Difference, and Integral Equations, Dordrecht, Kluwer Academic, 1999.
  • 2Avery R I, Henderson J. Three symmetric positive solutions for a second-order boundary value problem[J].Appl Math Lett, 2000,13 : 1--7.
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同被引文献18

  • 1Ma R Y, Zhang J H, Fu S M. The method of lower and upper solutions for fourth-order two-point boundary value problems[J]. J Math Anal Appl, 1997(215) :415 - 422.
  • 2Bai Z, Huang B, Ge W. The iterative solutions for some fourth-order p-Laplace equation boundary value problems[J]. Appl Math Lett, 2006(19):8- 14.
  • 3Ma D, Tian Y, Ge W. Existence theorems of positive solutions forfourth-order three-point boundary value problem[J]. Taiwan Residents J Math,2006,10(6) : 1557 - 1573.
  • 4葛谓高.非线性常微分方程边值问题[M].北京:科学出版社,2007.
  • 5郭大均．非线性泛函分析[M]．济南：山东科技出版社，2002．
  • 6Zhang Q,Chen S,Lu J. Upper and lower solution method for fourth-order four-point boundary value problems [j]. J Comput ApplMath, 2006(196) :387-393.
  • 7Bai Chuanzhi. Triple positive solutions of three-point boundary value problems for fourth-order differential equations Q]. AnalAppl, 2008 (56) :1364-1371.
  • 8Avery R L Henderson J. Two positive fixed points of nonlinear operators on ordered Banach spaces [J]. Appl Nonlinear Anal,2001(2):27-36.
  • 9D Ma, X Yang. Upper and lower solution method for four -order four -point boundary value problems [ J ], Comput. Appl. Math,2009 (223) : 543 - 551.
  • 10Q Zhang, S Chen, J Lti. Upper and lower solution method for fourth -order four -point boundary value problems [ J ]. Comput, Appl. Math,2006 (196) :387 -393.

引证文献6

二级引证文献8

数学的实践与认识
2007年 第24期

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