Poincaré-Hopf type formulas on convex sets of Banach spaces
Poincaré-Hopf type formulas on convex sets of Banach spaces
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DOI：
10.12775/tmna.2009.039
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发表时间：
2009-12
影响因子：
0.7
通讯作者：
T. Bartsch;Norman E. Dancer
中科院分区：
文献类型：
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作者：
T. Bartsch;Norman E. Dancer
我们考虑局部Lipschitz和完全连续的映射$A\colon C\to C$定义在Banach空间$X$的闭凸子集$C\子集X$上。主要的兴趣在于当$C$有空内部的情况。我们建立了Poincare-Hopf型公式，将$A$的不动点指数信息与$C$上由$-{\rmid}+A$诱导的半流的同调Conley指数信息联系起来.如果$A$是一个梯度，我们也得到结果的临界群的孤立不动点的$A$在$C$。
We consider locally Lipschitz and completely continuous maps $A\colon C\to C$ defined on a closed convex subset $C\subset X$ of a Banach space $X$. The main interest lies in the case when $C$ has empty interior. We establish Poincare-Hopf type formulas relating fixed point index information about $A$ with homology Conley index information about the semiflow on $C$ induced by $-{\rm id}+A$. If $A$ is a gradient we also obtain results on the critical groups of isolated fixed points of $A$ in $C$.