Periodic solutions of third-order degenerate differential equations with two infinite delays in vector-valued function spaces

Abstract

In this paper, we mainly study the well-posedness of third-order degenerate differential equations with two infinite delays in Lebesgue-Bochner spaces and periodic Besov spaces where A, B, L and M are closed linear operators on a Banach space X such that D(A) ∩ D(B) ⊂ D(M) ∩ D(L) and . We give necessary and sufficient conditions (P ₃) to be L^p -well-posed (resp. -well-posed and -well-posed) by using known operator-valued Fourier multiplier theorems.