Abstract view
Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces


Published:20180117
Printed: Dec 2018
Shangquan Bu,
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China
Gang Cai,
School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China
Abstract
We give necessary and sufficient
conditions of the $L^p$wellposedness (resp. $B_{p,q}^s$wellposedness) 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 $X$.
MSC Classifications: 
34G10, 34K30, 43A15, 47D06 show english descriptions
Linear equations [See also 47D06, 47D09] Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] $L^p$spaces and other function spaces on groups, semigroups, etc. Oneparameter semigroups and linear evolution equations [See also 34G10, 34K30]
34G10  Linear equations [See also 47D06, 47D09] 34K30  Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 43A15  $L^p$spaces and other function spaces on groups, semigroups, etc. 47D06  Oneparameter semigroups and linear evolution equations [See also 34G10, 34K30]
