Abstract
We study the existence of pseudo almost periodic mild solutions for the abstract evolution equation \(u'(t)=Au(t)+f(t,u(t))\), \(t\in\mathbb {R,}\) when the nonlinearity f satisfies certain critical conditions. We apply our abstract results to the heat equation.
Highlights
We observe that real systems usually exhibit internal variations or are submitted to external perturbations
In the literature several concepts have been studied to represent the idea of approximately periodic function
Most of the works deal with asymptotically periodic functions and almost periodic functions (e.g., [, ])
Summary
We observe that real systems usually exhibit internal variations or are submitted to external perturbations. Our purpose in this work is to analyze the existence of pseudo almost periodic mild solutions of the abstract problem u (t) = Au(t) + f t, u(t) , t ∈ R, In particular several results on the existence of pseudo almost periodic solutions to differential equations of the type
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