一类Banach空间中的指标理论及其应用

The Index Theory for a Class of Banach Spaces and Its Application

本文的主要目的是首先对一类具有特殊表示的Banach空间建立具有维数性质和规范性质的指标理论,然后,利用这个指标理论去考虑一类具有适当对称性的半线性椭园方程组的 Dirichlet 问题的多重解轨道的存在性.

The main purpose of this paper is first to establish the index theorywith dimensional and normal properties on the class of Banach spaces Xtogether with a special action of some compact Lie group G on X.andthen,apply this index theory to consider the existence of the multiplesolution orbits for the Dirichlet problem of a system of nonlinear ellipticequations.