Cordial Volterra Integral Equations with Vanishing Delays* - Journal of Applied Mathematics and Physics

JAMP > Vol.5 No.2, February 2017

Journal of Applied Mathematics and Physics

Volume 5, Issue 2 (February 2017)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Cordial Volterra Integral Equations with Vanishing Delays* ()

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Download as PDF (Size: 328KB) PP. 294-302

DOI: 10.4236/jamp.2017.52026 970 Downloads 1,923 Views

Author(s)

Hongjiu Wang^1,2*, Zhanwen Yang^2,3, Melusi Khumalo²

Affiliation(s)

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

ABSTRACT

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.

KEYWORDS

Cordial Volterra Integral Equations, Vanishing Delay, Propositional Delay, Compactness, Existence and Uniqueness

Share and Cite:

Wang, H. , Yang, Z. and Khumalo, M. (2017) Cordial Volterra Integral Equations with Vanishing Delays*. Journal of Applied Mathematics and Physics, 5, 294-302. doi: 10.4236/jamp.2017.52026.

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