正常的集值L-A-proper映射广义度及其应用

Generalized Degree of Normal Multivalued L-A-proper Mappings and its Applications

本文讨论Hilbert空间中半线性方程:z∈(L+N)u,L-线性闭稠定算子,N-集值映射。首先定义正常的集值L-A-proper映射,它们是[6]中L-A-proper映射的特殊子类,讨论与其有关的某些性质和相应的广义度的同伦不变性,应用这些理论对一类与有界dcmi-连续正常集值L-A-proper映射有关联的半线性映射建立了不动点定理。

In this paper, the semilinear equations Z∈ (L+N)u in Hilbert space where L-linear closed densely defined operator, N-a multivalued mapping have been studied.First, definition has been given to the normal multivalued L-A-proper mappings. They are a special subclass of L-A-proper mapping in paper [6]. Then some related properties and responding homotopy invariace of generalized degree have been discussed, with the application of these theories, the fixed point theorems have been established for the class of the semilinear mappings connected with the bounded, demi-continuous and normal multivalued L-A-proper mappings.