一類具有延遲中立型微分方程的漸近概自守溫和解

姚慧麗 李小桐 王晶囡 李雪鑫

摘 要：各類微分方程是基于不同實際問題而建立的數學模型，研究方程的各種解的存在問題引起了國內外數學學者的關注。利用Banach壓縮映射原理、概自守型函數的有關理論以及卷積族的指數二分性，針對一類具有延遲的中立型微分方程的漸近概自守溫和解的存在唯一性問題進行研究。漸近概自守溫和解比概自守溫和解更具有一般性，因此本文所研究問題會使這類方程的應用范圍更加廣泛。

關鍵詞：漸近概自守溫和解;中立型微分方程;Banach壓縮映射原理

DOI：10.15938/j.jhust.2021.04.021

中圖分類號：O177.92

文獻標志碼：A

文章編號：1007-2683（2021）04-0153-06

Abstract：All kinds of differential equations as mathematical models have been built up due to different practical problems， so the problem of studying the existence of various solutions has attracted the attention of ?mathematical scholars at home and abroad. The problem on the existence and uniqueness of asymptotically almost automorphic mild solutions for a class of neutral differential equations with delay are researched by using Banach compression mapping principle， related theorems of almost automorphic type functions and the exponential dichotomy of convolution family in this paper. Asymptotically almost automorphic mild solutions are more general than almost automorphic mild solutions， so the research of this paper will make the scope of application on this kind of differential equations more extensive.

Keywords：asymptotically almost automorphic mild solutions; neutral differential equations; Banach compression mapping principle

0 引 言

微分方程是多學科研究領域常用的工具，如數學、物理學、化學、生物學等。其中，要研究的多數問題都可以轉化為探討微分方程的各類解的存在性問題。目前為止已有大量文獻對各類微分方程的概周期型解[1-6]，概自守溫和解[7-11]、以及偽概自守溫和解[12-15]進行了研究。

3 結 論

本文利用Banach壓縮映射原理、卷積族的指數二分性及概自守型函數的有關性質證明了一類具有延遲的中立型微分方程在適當的條件下存在唯一的漸近概自守溫和解。

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（編輯：溫澤宇）