On a weakly singular quadratic integral equations of Volterra type in Banach algebras

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• 作者：Xiulan Yu (16)
  Chun Zhu (17)
  JinRong Wang (17) (18)
  
  16. College of Applied Mathematics ; Shanxi University of Finance and Economics ; Taiyuan ; Shanxi ; 030031 ; P.R. China
  17. Department of Mathematics ; Guizhou University ; Guiyang ; Guizhou ; 550025 ; P.R. China
  18. Industrial Internet of Things Engineering Research Center of the Higher Education Institutions of Guizhou Province and School of Mathematics and Computer Science ; Guizhou Normal College ; Guiyang ; Guizhou ; 550018 ; P.R. China
  
• 关键词：weakly singular quadratic integral equations ; Banach algebras ; measure of noncompactness ; fixed point theorem
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：286 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we present existence and uniqueness theorems of nonnegative, asymptotically stable, and ultimately nondecreasing solutions for weakly singular quadratic integral equations of Volterra type in Banach algebras. The concept of the measure of noncompactness and a fixed point theorem due to Darbo acting in a Banach algebra are the main tools in carrying out our proof. An effective numerical example is given to illustrate our theory results. MSC: 45G05, 47H30.