Periodic Solutions of Third‐Order Mixed Degenerate Differential Equations With Two Infinite Delays in Vector‐Valued Function Spaces

ABSTRACT The aim of this paper is to consider the well‐posedness of third‐order mixed degenerate differential equation with two infinite delays : in Lebesgue–Bochner spaces and periodic Besov spaces , where , , , and are closed linear operators on a Banach space satisfying and . Necessary and sufficient conditions for to be ‐well‐posed (or ‐well‐posed) are given by using known operator‐valued Fourier multiplier theorems.