New Variation of Constants Formula for Some Partial Functional Differential Equations with Infinite Delay
Abstract
In this work, we give a new variation of constants formula for some partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. When the phase space is a uniform fading memory space, we establish a spectral decomposition of the phase space. This allows us to study the existence of almost periodic solutions when the equation has a bounded solution on the half line $\mathbb{R}^+$
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