含有广义p-Laplace算子具混合边值条件的积分微分方程解的存在唯一性(英文)  

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO INTEGRO-DIFFERENTIAL EQUATION INVOLVING THE GENERALIZED p-LAPLACIAN OPERATOR WITH MIXED BOUNDARY CONDITIONS

作　　者：魏利[1] 段丽凌[1] Ravi P.Agarwal 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]Department of Mathematics, Texas Agricultural and Mechanical University-Kingsville

出　　处：《数学杂志》2013年第6期1009-1018,共10页Journal of Mathematics

基　　金：Supported by by National Natural Science Foundation of China(11071053);the Natural Science Foundation of Hebei Province(A2010001482);the Key Project of Science and Research of Hebei Education Department(ZH2012080)

摘　　要：本文研究了一类含有广义p-Laplace算子、具有混合边值条件的积分微分方程.运用将积分微分方程分解为非线性算子的研究方法,获得了这类方程解的存在唯一性的结论.与以往相关工作相比,不仅得到了解的存在性,还证明了解的唯一性.同时摒弃了传统的有限元法,而改用极大单调算子和伪压缩算子的值域理论研究问题,从而推广和补充了以往的研究工作.One kind of integro-differential equations involving the generalized p-baplaclan operator with mixed boundary conditions is studied in this paper. The method of decomposing the integro-differential equation to the nonlinear operators are employed and the existence and uniqueness of the solution are obtained. Compared to the previous work on this topic, not only existence but also the uniqueness of the solution is obtained. Moreover, some techniques and results on the ranges of maximal monotone operators and pseudo-monotone operators are employed instead of the finite element method, which extend and complement some previous works.

关 键 词：极大单调算子 伪单调算子 广义p-拉普拉斯算子 具有混合边值条件的积分微分方程 

分 类 号：O177.91[理学—数学]