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

Published online by Cambridge University Press:  19 September 2016

Shangquan Bu
Affiliation:
Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, People's Republic of China ([email protected])
Gang Cai*
Affiliation:
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, People's Republic of China ([email protected])
*
*Corresponding author.

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].

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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