非线性椭圆边值问题和极大单调算子的零点(英文)

Nonlinear Elliptic Boundary Value Problems and Zero Point of Maximal Monotone Operators

本文利用非线性极大单调算子值域的扰动结论,研究一类与广义p-Laplacian算子相关的、具Neumann边值条件的非线性椭圆方程的解的存在唯一性.同时研究这个唯一解与适当定义的非线性极大单调算子的零点之间的关系.进而设计一种迭代算法强收敛到这个唯一解本文采用新的构造算子和拆分方程的方法。

By using perturbation results on the ranges of nonlinear maximal monotone operators,we present an Abstract result for the existence and uniqueness of the solutions of nonlinear elliptic equation with Neumann boundary value conditions involving the generalized p-Laplacian operator in this paper.The relationship between the unique solution and the zero point of a suitably defined nonlinear maximal monotone operator is investigated.Moreover,an iterative scheme is constructed to be strongly convergent to the unique solution.Some new techniques of constructing appropriate operators and decomposing the equations are employed,which extend and complement some of the previous work.