Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T17:55:36.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Well-Posedness of Second-Order Degenerate Differential Equations with Finite Delay

Part of: Differential equations in abstract spaces Groups and semigroups of linear operators, their generalizations and applications Functional-differential and differential-difference equations

Published online by Cambridge University Press:  19 September 2016

Shangquan Bu  and
Gang Cai
Shangquan Bu
Affiliation:
Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, People's Republic of China (sbu@math.tsinghua.edu.cn)
Gang Cai*
Affiliation:
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People's Republic of China (caigang-aaaa@163.com)
*
*Corresponding author.
Get access Rights & Permissions [Opens in a new window]

Abstract

We give necessary and sufficient conditions for the Lp-well-posedness of the second-order degenerate differential equations with finite delay

with periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′(0) = (Mu)′(2π). Here A and M are closed operators on a complex Banach space X satisfying D(A) ⊂ D(M), α ∈ ℂ is fixed, F is a bounded linear operator from Lp([−2π, 0],X) into X, and ut is given by ut(s) = u(t + s) when s ∈ [−2π, 0].

Keywords

degenerate differential equation with delayLp-well-posednessLebesgue–Bochner spacesFourier multipliers

MSC classification

Secondary: 34G10: Linear equations 47D06: One-parameter semigroups and linear evolution equations 34K13: Periodic solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 349 - 360
Copyright
Copyright © Edinburgh Mathematical Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)