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

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.