全连续算子与拓扑度的相关证明及实例探究

The Related Proof and Case Study of Completely Continuous Operator and Topological Degree

非线性泛函是现代数学研究中很重要的工具,非线性泛函分析包括拓扑度理论、半序方法、变分方法、分歧理论和Banach空间微分方程理论,本文讨论非线性算子的连续性与有界性,全连续算子与拓扑度相关性质的证明,并用实例证明相关结论.

Nonlinear functional analysis is an important tool in the study of modem mathematics. Nonlinear functional analysis includes the theory of topological degree, the semi order method, the variational method, the theory of bifurcation and differential equation theory in Banaeh space. The paper discusses how to prove the related properties of continuity and boundedness of nonlinear operator, completely continuous operator and topological degree. I give examples to prove the conclusions.