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arXiv · 2209.10220

On a class of retarded integrodifferential equations

Fouad Maragh
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Abstract

The following class of retarded integro-differential equations in a Banach space \[ \dot{x}\left(t\right)=Ax\left(t\right)+\int_{0}^{t}b\left(t-τ\right)Lx_τdτ+Kx_{t};\,\,t\geq0, \] are taken into consideration in this study. The delay term $Lx_τ$ of this equation is inserted into the integral as a convolution product with a scalar kernel. We prove the well-posedness of the problem under investigation using the Miyadera-Voigt perturbation and the theory of semigroups. We also explore the spectral analysis of an associated abstract Cauchy problem.

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Fouad Maragh. 2023-01-30. On a class of retarded integrodifferential equations. https://arxiv.org/abs/2209.10220

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