Periodic solutions of integro-differential equations in Banach space\n having Fourier type

2017/06/26 by Bahloul Rachid, Rachid, Bahloul
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1708.05608

openalex publication_date 2017/06/26 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to study the existence of a periodic solutions of\nintegro-differential equations d dt [x(t)-- L(x t)] = A[x(t)-- L(x t)]+ G(x t)+\nt --\∞ a(t-- s)x(s)ds+ f (t), (0 \≤ t \≤ 2\π) with the periodic\ncondition x(0) = x(2\π), where a \∈ L 1 (R +). Our approach is based on\nthe M-boundedness of linear operators, Fourier type, B s p,q-multipliers and\nBesov spaces.\n

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