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Computers & Mathematics with Applications
Volume 54, Issue 1, July 2007, Pages 58-75
 
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doi:10.1016/j.camwa.2006.10.031    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2007 Elsevier Ltd All rights reserved.

Constant-sign solutions of a system of Volterra integral equations

Ravi P. Agarwala, Corresponding Author Contact Information, E-mail The Corresponding Author, Donal O’Reganb, E-mail The Corresponding Author, Christopher C. Tisdellc, E-mail The Corresponding Author and Patricia J.Y. Wongd, E-mail The Corresponding Author

aDepartment of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA bDepartment of Mathematics, National University of Ireland, Galway, Ireland cSchool of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia dSchool of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Received 5 October 2006; 
accepted 18 October 2006. 
Available online 2 April 2007.

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Abstract

We consider the following system of Volterra integral equations:

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and some of its particular cases that arise from physical problems. Criteria are offered for the existence of one and more constant-sign solutions u=(u1,u2,…,un) of the system in (C[0,T])n. We say u is of constant sign if for each 1≤i≤n,θiui(t)≥0 for all tset membership, variant[0,T], where θiset membership, variant{1,−1} is fixed. Examples are also included to illustrate the results obtained.

Keywords: Constant-sign solutions; System of Volterra integral equations; Singular Volterra integral equations

Article Outline

1. Introduction
2. Existence results for (1.1)
3. Existence results for (1.2) and (1.3)
4. Existence results for (1.4)
Acknowledgements
References

Computers & Mathematics with Applications
Volume 54, Issue 1, July 2007, Pages 58-75
 
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