含有广义p-Laplace算子的非线性边值问题解的存在性的研究

数学物理学报 ›› 2012, Vol. 32 ›› Issue (1): 201-211.

含有广义p-Laplace算子的非线性边值问题解的存在性的研究

魏利, Ravi P Agarwal

河北经贸大学数学与统计学学院石家庄 050061|Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

收稿日期:2010-11-29 修回日期:2011-10-18 出版日期:2012-02-25 发布日期:2012-02-25
基金资助:
国家自然科学基金(11071053)、河北省自然科学基金(A2010001482)和河北省教育厅科学研究计划项目(2010第二批)资助

Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator

魏利, Ravi P Agarwal

School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061|Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

Received:2010-11-29 Revised:2011-10-18 Online:2012-02-25 Published:2012-02-25
Supported by:
国家自然科学基金(11071053)、河北省自然科学基金(A2010001482)和河北省教育厅科学研究计划项目(2010第二批)资助

摘要/Abstract

摘要：

该文研究了两类含有广义p-Laplace算子的非线性边值问题. 首先, 利用变分不等式解的存在性的结果, 证明了含有广义p-Laplace算子的非线性Dirichlet边值问题解的存在性. 然后, 提出了一类含有广义p-Laplace算子的非线性Neumann边值问题. 通过深入挖掘这两类非线性边值问题间的关系, 借助于极大单调算子值域的一个扰动结果, 证明了含有广义p-Laplace算子的非线性Neumann边值问题解的存在性. 文中采用了一些新的证明技巧，推广和补充了作者以往的一些研究工作.

关键词: 极大单调算子, hemi连续映射, 广义p-Laplace算子, 值域和, 非线性Dirichlet 或Neumann 边值问题

Abstract:

Two kinds of nonlinear boundary value problems with generalized p-Laplacian operator are studied in this paper. By using a result on the existence of solutions for variational inequalities, the result on the existence of solution of the nonlinear Dirichlet boundary value problem with generalized p-Laplacian operator is proved. Later, a kind of nonlinear Neumann boundary value problem with generalized p-Laplacian operator is presented. By digging deeply into the relationship between the above two kinds of nonlinear boundary value problems and by using a perturbation resulton the ranges of maximal monotone operators, an abstractresult for the existence of solution of the nonlinear Neumann boundary value problem with generalized p-Laplacianoperatoris obtained. In this paper, somenew prooftechniques areemployed, which extend and complement some of the previous research work.

Key words: Maximal monotone operator, Hemi-continuousmapping, Generalized p-Laplacian operator, Sum of ranges, Nonlinear Dirichlet (Neumann) boundary value problem

中图分类号:

47H09

魏利, Ravi P Agarwal. 含有广义p-Laplace算子的非线性边值问题解的存在性的研究[J]. 数学物理学报, 2012, 32(1): 201-211.

WEI Li, Ravi P Agarwal. Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator[J]. Acta mathematica scientia,Series A, 2012, 32(1): 201-211.

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