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

Advances in Difference Equations

Xiulan Yu¹  Chun Zhu²  JinRong Wang² 

[1] College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, P.R. China;Department of Mathematics, Guizhou University, Guiyang, P.R. China

关键词: weakly singular quadratic integral equations;    Banach algebras;    measure of noncompactness;    fixed point theorem;   

DOI  :  10.1186/1687-1847-2014-130

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY