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Stepanov-Almost Periodic Solutions of Non-autonomous Neutral Functional Differential Equations with Functional Delay

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Abstract

In this paper, we study the existence and uniqueness of Stepanov-almost periodic mild solution to the non-autonomous neutral functional differential equation

$$\begin{aligned} \frac{{\hbox {d}}}{\hbox {d}t}[u(t)-F(t,u(t-\alpha (t)))]= & {} A(t)[u(t)-F(t,u(t-\alpha (t)))]\\&+\,G(t,u(t),u(t-\alpha (t))),\quad t\in \mathbb {R}, \end{aligned}$$

in a Banach space \(\mathbb {X},\) where the family of linear operators A(t) satisfies the ‘Acquistapace–Terreni’ conditions, the evolution family generated by \(A(t),t\in \mathbb {R},\) is exponentially stable, \((\gamma -A(\cdot ))^{-1}\) and \(\alpha (\cdot )\) are almost periodic, and F and G are Stepanov-almost periodic continuous functions.

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  1. Department of Mathematics, National Institute of Technology Silchar, Cachar, Assam, 788010, India

    Md. Maqbul

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  1. Md. Maqbul
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Maqbul, M. Stepanov-Almost Periodic Solutions of Non-autonomous Neutral Functional Differential Equations with Functional Delay. Mediterr. J. Math. 15, 179 (2018). https://doi.org/10.1007/s00009-018-1224-7

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  • DOI: https://doi.org/10.1007/s00009-018-1224-7

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