Integral Inequalities and Pseudo Almost Automorphic Solutions to Semilinear Differential Equations in Banach Spaces

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• 作者：Jung-Chan Chang ; Dah-Chin Luor
• 关键词：Integral inequality ; pseudo almost automorphic function ; compact semigroup ; mild solution
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：13
• 期：6
• 页码：4353-4368
• 全文大小：550 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

This work aims to investigate the existence and uniqueness of pseudo almost automorphic solutions to semilinear differential equations in Banach space. By generalizing the Bihari type inequality and using Krasnoselski–Schaefer fixed point theorem, the existence results are deduced. Moreover, a new estimate is also built to ensure the existence and uniqueness of solutions. An example is given to illustrate our conclusions.