Vol. 288, No. 1, 2017

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ISSN: 0030-8730
Well-posedness of second-order degenerate differential equations with finite delay in vector-valued function spaces

Shangquan Bu and Gang Cai

Vol. 288 (2017), No. 1, 27–46
Abstract

We give necessary and sufficient conditions of the Lp-well-posedness (respectively, Bp,qs-well-posedness) for the second-order degenerate differential equation with finite delay: (Mu)(t) + αu(t) = Au(t) + Gut + Fut + f(t), (t [0,2π]) with periodic boundary conditions u(0) = u(2π), (Mu)(0) = (Mu)(2π), where A and M are closed linear operators on a Banach space X satisfying D(A) D(M), and F and G are bounded linear operators from Lp([2π,0];X) (respectively, Bp,qs([2π,0];X)) into X.

Keywords
Degenerate differential equations, delay equations, well-posedness, Lebesgue–Bochner spaces, Besov spaces, Fourier multipliers
Mathematical Subject Classification 2010
Primary: 34G10, 34K30, 43A15, 47D06
Milestones
Received: 12 April 2016
Accepted: 25 August 2016
Published: 8 April 2017
Authors
Shangquan Bu
Department of Mathematical Sciences
Tsinghua University
100084 Beijing
China
Gang Cai
School of Mathematical Sciences
Chongqing Normal University
401331 Chongqing
China