Well‐posedness of second‐order degenerate differential equations with finite delay on Lp(ℝ;X)$$ {L}^p\left(\mathbb{R};X\right) $$

Abstract

Using operator‐valued ‐Fourier multiplier theorem, weighted Sobolev spaces, and the Carleman transform, we characterize the well‐posedness of second‐order degenerate differential equations with finite delay on , where and are closed linear operators defined on a Banach space , the operators and are in for some fixed , and when and . These results are used to study the well‐posedness of the associated second‐order neutral degenerate differential equations.