Periodic solutions of second‐order degenerate differential equations with infinite delay in Banach spaces

Author:

Bu Shangquan1,Cai Gang2

Affiliation:

1. Department of Mathematical Sciences Tsinghua University Beijing China

2. School of Mathematical Sciences Chongqing Normal University Chongqing China

Abstract

AbstractWe consider the well‐posedness of the second‐order degenerate differential equations with infinite delay on [0, 2π] in Lebesgue–Bochner spaces and periodic Besov spaces , where , and M are closed linear operators in a Banach space X satisfying and the kernels . Using known operator‐valued Fourier multiplier theorems, we are able to give necessary and sufficient conditions for the well‐posedness of (P) in and . These results are applied to examine some concrete examples.

Funder

Natural Science Foundation of Chongqing

National Natural Science Foundation of China

Publisher

Wiley

Subject

General Mathematics

Reference23 articles.

1. Perturbation Method for First- and Complete Second-Order Differential Equations

2. Decay estimates for second order differential equations with memory;Alabau‐Boussouira F.;J. Diff. Equ.,2008

3. Operator-Valued Fourier Multipliers, Vector - Valued Besov Spaces, and Applications

4. Lp$L^p$‐maximal regularity for a class of degenerate integro‐differential equations with infinite delay in Banach spaces;Aparicio R.;J Fourier Anal. Appl.,2020

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