极大单调算子和m增生映射值域的扰动定理及在非线性微分方程上的应用  

The Perturbation Theories of Ranges for Maximal Monotone Operators and m-Accretive Mappings and their Applications to Nonlinear Differential Equation

作　　者：魏利[1] 

机构地区：[1]河北经贸大学数学与统计学学院应用数学教研室

出　　处：《数学的实践与认识》2006年第4期232-239,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(10471033)

摘　　要：利用不动点定理,分别证明了在自反Banach空间中极大单调算子值域扰动的抽象结论和在H ilbert空间中m增生映射值域的扰动结果,这些结论是对以往一些工作的推广;然后,利用文中的新结论讨论了一类微分方程解的存在性.By using the fixed point theorems, some abstract results on perturbations of ranges for maximal monotone operators in reflexive Banach space and for m-accretive mappings in Hilbert space which are improvement to some previous works are given. Later, the existence of the solution of one kinds of differential equations is discussed by using the new results given in this paper.

关 键 词：极大单调算子 紧映射 demi连续映射 增生映射 对偶映射 

分 类 号：O177[理学—数学]