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Bu, Shangquan; Cai, Gang
Periodic solutions of second order degenerate differential equations with delay in Banach spaces
We give necessary and sufficient conditions of the $L^p$-well-posedness (resp. $B_{p,q}^s$-well-posedness) for the second order degenerate differential equation with finite delays: $(Mu)''(t)+Bu'(t)+Au(t)=Gu'_t+Fu_t+f(t),(t\in [0,2\pi])$ with periodic boundary conditions $(Mu)(0)=(Mu)(2\pi)$, $(Mu)'(0)=(Mu)'(2\pi)$, where $A, B, M$ are closed linear operators on a complex Banach space $X$ satisfying $D(A)\cap D(B)\subset D(M)$, $F$ and $G$ are bounded linear operators from $L^p([-2\pi,0];X)$ (resp. $B_{p,q}^s([-2\pi,0];X)$) into $X$.

Keywords:second order degenerate differential equation, Fourier multiplier theorem, well-posedness, Lebesgue-Bochner space, Besov space
Categories:34G10, 34K30, 43A15, 47D06

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