含有广义p-Laplace算子的非线性边值问题解的存在性的研究  

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

作　　者：魏利[1] Ravi P Agarwal 

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061 [2]Department of Mathematical Sciences,Florida Institute of Technology,Melbourne,FL 32901,USA

出　　处：《数学物理学报（A辑）》2012年第1期201-211,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11071053);河北省自然科学基金(A2010001482);河北省教育厅科学研究计划项目(2010第二批)资助

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.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 result on the ranges of maximal monotone operators, an abstract result for the existence of solution of the nonlinear Neumann boundary value problem with generalized p-Laplacian operator is obtained. In this paper, some new proof techniques are employed, which extend and complement some of the previous research work.

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. 

分 类 号：O177.91[理学—数学]