含有广义p-Laplace算子的非线性边值问题解的存在性的研究 |
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引用本文: | 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(A辑), 2012, 32(1): 201-211 |
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作者姓名: | 魏利 Ravi P Agarwal |
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作者单位: | 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 |
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基金项目: | 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 |
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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.
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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 |
收稿时间: | 2010-11-29 |
修稿时间: | 2011-10-18 |
Discussion on the Existence of Solution to Nonlinear Boundary Value Problem with Generalized p-Laplacian Operator |
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Affiliation: | 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 |
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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. |
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Keywords: | Maximal monotone operatorzz Hemi-continuousmappingzz Generalized p-Laplacian operatorzz Sum of rangeszz Nonlinear Dirichlet (Neumann) boundary value problemzz |
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