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Multiple Positive Solutions to a Nonlinear Two-point Boundary Value Problem with p-Laplacian 被引量:4

p-Laplace非线性两点边值问题多个正解的存在性(英文)
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摘要 By a simple application of a new three functionals fixed point theorem, sufficient conditions axe obtained to guarantee the existence of at least three positive solutions for p-Laplacian equation: (φp(u′))′ + α(t)f(t,u(t)) = 0 subject to nonlinear boundary value conditions. An example is presented to illustrate the theory. 本文利用一种新的三个泛函不动点定理得到了p-Laplacian方程在具有非线性边值条件时至少存在三个正解的充分条件,并且举了一个简单例子来说明得到的结论.
出处 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2006年第3期480-488,共9页 数学研究与评论(英文版)
基金 the National Natural Science Foundation of China (10371006)
关键词 boundary value problem p-Laplacian operator positive solution the threefunctionals fixed point theorem. 边值问题 p-Laplacian算子 正解 三个泛函不动点定理
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参考文献6

  • 1HE Xiao-ming,GE Wei-gao.Twin positive solutions for the one-dimensional p-Laplacian boundary value problems[J].Nonlinear Anal.,2004,56:975-984.
  • 2GUO Yan-ping,GE Wei-gao.Three positive solutions for the one-dimensional p-Laplacian[J].J.Math.Anal.Appl.,2003,286:491-508.
  • 3HE Xiao-ming,GE Wei-gao.Triple solutions for second-order three-point boundary value problems[J].J.Math.Anal.Appl.,2002,268:256-265.
  • 4AVERY R I,HENDSON J.Two positive fixed points of nonlinear operators on ordered Banach spaces[J].Comm.Appl.Nonlinear Anal.,2001,8:27-36.
  • 5REN Jing-li.Fixed point theorems and boundary value problems of differential equation[D].Doctoral Papers of Beijing Institute of Technology,Beijing,2004.(in Chinese)
  • 6WANG Jun-yu.The existence of positive solutions for the one-dimensional p-Laplacian[J].Proc.Amer.Math.Soc.,1997,125:2275-2283.

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