Cordial Volterra Integral Equations with Vanishing Delays  

作　　者：Hongjiu Wang Zhanwen Yang Melusi Khumalo 

机构地区：[1]College of Science, Heilongjiang University of Science and Technology, Harbin, China [2]Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park, Johannesburg, South Africa [3]Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Har-bin, China

出　　处：《Journal of Applied Mathematics and Physics》2017年第2期294-302,共9页应用数学与应用物理（英文）

摘　　要：Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.

关 键 词：CORDIAL VOLTERRA Integral Equations VANISHING DELAY Propositional DELAY COMPACTNESS Existence and UNIQUENESS 

分 类 号：O1[理学—数学]