与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性及其迭代构造(英文)  

Existence and Iterative Construction of Solutions for Nonlinear Dirichlet Elliptic Systems Involving(p,q)-Laplacian

作　　者：魏利[1] 刘元星[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 Mathematical Sciences Florida Institute of Teehnology,Melbourne,FL 32901 U.S.A.

出　　处：《应用数学》2012年第2期246-252,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11071053);the Natural Science Foundation of Hebei Province(A2010001482);the Project of Science and Research of Hebei Education Department(the second round in 2010)

摘　　要：利用变分不等式解的存在性的结论,研究了一类与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性的抽象结论.然后,利用极大单调算子零点的结论,构造了一种迭代格式强收敛到上述椭圆系的解.本文所研究的椭圆系及所用方法是对以往一些工作的推广和补充.By using the result on the existence of solutions for variational inequalities, we present some abstract results for the existence of the solutions o~ nonlinear Dirichlet elliptic systems invol- ving （p, q） -Laplacian. By using a result on zero points of maximal monotone operators, we construct an iterative scheme to be convergent strongly to the solutions of the above systems. The systems discussed in this paper and the method used extend and complement some o~ the previous work.

关 键 词：极大单调算子 伪单调算子 (p  q)-Laplace算子 零点 非线性Dirichlet椭圆系 

分 类 号：O177.91[理学—数学]