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Fall 2020 Solutions of second-order degenerate equations with infinite delay in Banach spaces
Shangquan Bu, Gang Cai
J. Integral Equations Applications 32(3): 259-274 (Fall 2020). DOI: 10.1216/jie.2020.32.259

Abstract

We consider the well-posedness of the second-order degenerate differential equations with infinite delay (P2): (Mu)(t)+(Lu)(t)=Au(t)+ta(ts)Bu(s)ds+f(t), (0t2π) with periodic boundary conditions u(0)=u(2π), (Mu)(0)=(Mu)(2π), in Lebesgue–Bochner spaces Lp(𝕋;X) and periodic Besov spaces Bp,qs(𝕋;X), where A, B, L and M are closed linear operators in a Banach space X satisfying D(A)D(B)D(M)D(L), D(A)D(B){0} and aL1(+). We completely characterize the well-posedness of (P2) in the above function spaces by using known operator-valued Fourier multiplier theorems. We also give concrete examples to support our abstract results.

Citation

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Shangquan Bu. Gang Cai. "Solutions of second-order degenerate equations with infinite delay in Banach spaces." J. Integral Equations Applications 32 (3) 259 - 274, Fall 2020. https://doi.org/10.1216/jie.2020.32.259

Information

Received: 7 May 2019; Revised: 18 November 2019; Accepted: 12 December 2019; Published: Fall 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07283057
MathSciNet: MR4150700
Digital Object Identifier: 10.1216/jie.2020.32.259

Subjects:
Primary: 34G10, 34K30, 43A15, 47D06

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 3 • Fall 2020
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