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首页> 外文期刊>Journal of Differential Equations >Topological degree methods for perturbations of operators generating compact C-0 semigroups
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Topological degree methods for perturbations of operators generating compact C-0 semigroups

机译：生成紧致C-0半群的算子扰动的拓扑度方法

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摘要

The main aim of this paper is to construct a topological degree for maps -A + F : M boolean AND D(A) -> E where a densely defined closed operator A : D(A) -> E of a Banach space E is such that -A is the generator of a compact C-0 semigroup, and F : M -> E is a locally Lipschitz map defined on a neighborhood retract M subset of E. If M is a closed convex cone, then a degree formula allowing an effective computation of the degree is proved. This formula provides an infinite-dimensional counterpart of the well-known Krasnosel'skii theorem. By the use of the introduced topological degree and an abstract result concerning branching of fixed points, the bifurcation of periodic points of the parameterized boundary value problem
机译：本文的主要目的是构造映射-A + F：M布尔AND D（A）-> E的拓扑度，其中密定义封闭算子A：D（A）-> E的Banach空间E为因此，-A是紧致的C-0半群的生成器，而F：M-> E是在E的邻域收缩M子集上定义的局部Lipschitz映射。证明了该度数的有效计算。该公式提供了著名的Krasnosel'skii定理的无穷维对应。通过使用引入的拓扑度和关于固定点分支的抽象结果，参数化边值问题的周期点分叉

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