含有广义p-Laplacian算子的非线性椭圆边值问题和m增生映射的值域

Nonlinear Elliptic Boundary Value Problems with Generalized p-Laplacain and Range of m-Accretive Mappings

证明了m增生映射的一个值域扰动结论并用于讨论一类含有广义p-Laplacian算子的非线性椭圆边值问题在L^2（Ω）中解的存在性．探究了非线性椭圆边值问题的解与m增生映射零点的关系．构造了迭代序列用以弱收敛或强收敛到非线性椭圆边值问题的解．本文采用了构造新算子和拆分方程的技巧，推广和补充了以往的相关研究成果．

A perturbation result on the ranges of m-accretive mappings is proved and used to show that a family of nonlinear elliptic boundary value problems with the generalized p-Laplacian operator have solutions in L2（Ω）. The relationship between the solution and the zero point of a suitably defined nonlinear m- accretive mapping is investigated. Moreover, some iterative schemes are constructed to be weakly or strongly convergent to the solution. Some new techniques of constructing appropriate operators and decomposing the equations are employed, which extend and complement some of the previous work.