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具p-Laplacian的四点边值问题三个正解的存在性

Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem With p-Laplacian
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摘要 利用Avery-Peterson不动点定理,建立了一类奇异非线性p-Laplace方程在某些边值条件下至少存在三个正解的充分条件,推广和改进了现有文献的一些结果. This paper deals with a class of singular p-Laplacian equation （φp（u＇（t）））＇＋a（t）f（t,u（t）,u＇（t））=0,0〈t〈1 subject to the following nonlinear boundary conditions αφp（u（0））-βφp（u＇（ξ））=0,γφp（u（1））＋δφp（u＇（η））=0, where φp（x） = ｜x｜^p-2x, p 〉 1. By using the Avery-Peterson fixed point theorem, sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are established. The recent results are generalized and improved.
作者 李相锋 赵培浩
机构地区 兰州大学数学与统计学院 陇东学院数学系
出处 《数学进展》 CSCD 北大核心 2009年第2期146-156,共11页 Advances in Mathematics（China）
基金 甘肃省高校研究生导师科研基金(No.0710-04,No.0810-03).
关键词 P-LAPLACIAN算子 Avery—Peterson不动点定理 正解 边值问题 p-Laplacian operator Avery-Peterson fixed-point theorem positive solutions boundary value problem
分类号 O175.8 [理学—基础数学]
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参考文献12

  • 1Bai Z.B. and Ge W.G., Existence of three positive solutions for the one-dimensional p-Laplemian, Acta MathemaSica Sinica, Chinese Series, 2006, 49(5): 1045-1052
  • 2Sun B. and Ge W.G., Existence and iteration of positive solutions for some p-Laplacian boundary value problems, Nonlinear Analysis, 2007, 67: 1820-1830.
  • 3Bai Z.B., Gui Z.J. and Ge W.G., Multiple positive solutions for some p-Laplacian boundary value problems, J. Math. Anal. Appl., 2004, 300: 477-490.
  • 4Xiong M. and Wang S.R., The existence of positive solution for the one-dimensional p-Laplacian, Acta Mathematica Sinica, Chinese Series, 2006, 49(1): 162-168.
  • 5Li Z.Y., Yan S.L. and Ge W.G., Multiple positive solutions to a nonlinear two-point boundary value problem with p-Laplacian, J. Math. Research and Exposition, 2006, 26(3): 480-488.
  • 6Zhao D.X., Wang H.Z. and Ge W.G., Existence of triple positive solutions to a class of p-Laplacian boundary value problems, J. Math. Anal. Appl., 2007, 328: 972-983.
  • 7Ma D.X., Han J.X. and Chen X.G., Positive solutions of thrEe-point boundary value problem for the one-dimensional p-Laplacian with singularities, J. Math. Anal. Appl., 2006, 324: 118-133.
  • 8Li X.F., Multiple positive solutions for some four-point boundary value problems with p-Laplacian, Applied Mathematics and Computation, 2008, 202: 413-426.
  • 9Ji D.H. and Ge W.G., Existence of multiple positive solutions for Sturm-Liouville-like four-point boundary value problem with p-Laplacian, Nonlinear Analysis, 2008, 68: 2638-2646.
  • 10Ji D.H. and Ge W.G., Multiple positive solutions for some p-Laplacian boundary value problems, Applied Mathematics and Computation, 2007, 187: 1315-1325.
数学进展
2009年 第2期

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