Article ID Journal Published Year Pages File Type
4614921 Journal of Mathematical Analysis and Applications 2016 14 Pages PDF
Abstract

Using an ergodic approach, we investigate the condition for existence and uniqueness of periodic solutions to linear evolution equation u˙=A(t)u+f(t), t≥0t≥0, and to semi-linear evolution equations of the form u˙=A(t)u+g(u)(t), where the operator-valued function t↦A(t)t↦A(t) and the vector-valued function f(t)f(t) are T-periodic, and Nemytskii's operator g is locally Lipschitz and maps T-periodic functions to T  -periodic functions. We then apply the results to study the existence, uniqueness, and conditional stability of periodic solutions to the above semi-linear equation in the case that the family (A(t))t≥0(A(t))t≥0 generates an evolution family having an exponential dichotomy.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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