Well-Posedness of Second-Order Degenerate Differential Equations with Finite Delay
Shangquan Bu, Gang Cai · Proceedings of the Edinburgh Mathematical Society · 2016
Abstract We give necessary and sufficient conditions for theLp-well-posedness of the second-order degenerate differential equations with finite delay with periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′(0) = (Mu)′(2π). HereAandMare closed operators on a complex Banach spaceXsatisfyingD(A) ⊂D(M),α ∈ℂ is fixed,Fis a bounded linear operator fromLp([−2π,0],X) intoX, andutis given byut(s) =u(t+s) whens ∈[−2π,0].