Fredholm operators, evolution semigroups, and periodic solutions of nonlinear periodic systems
Fredholm operators, evolution semigroups, and periodic solutions of nonlinear periodic systems
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Fredholm 算子、演化半群和非线性周期系统的周期解
DOI：
10.1016/j.jde.2014.08.007
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发表时间：
2014
影响因子：
2.4
通讯作者：
T. Naito and J. S. Shin
中科院分区：
文献类型：
--
作者：
R. Miyazaki;D. Kim;T. Naito and J. S. Shin
设X是Banach空间，L是所有τ周期连续X值函数在Pτ(X)上的τ周期演化过程{U(t，S)}t≥S的演化半群的生成元.在1是单调算子U(−ϵ，0)的正规本征值的条件下，给出了形式为L p=ϵF(p，τ)的非线性系统周期解的存在性准则。证明是基于空间Pτ(X)的一种新的分解，即构造L的右逆。
Let X be a Banach space and L the generator of the evolution semigroup associated with the τ-periodic evolutionary process {U (t, s)} t≥ s on the space P τ (X) of all τ-periodic continuous X-valued functions. We give criteria for the existence of periodic solutions to nonlinear systems of the form L p=− ϵ F (p, ϵ) under the condition that 1 is a normal eigenvalue of the monodromy operator U (τ, 0). The proof is based on a new decomposition of the space P τ (X) by constructing a right inverse of L.