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NONTRIVIAL PERIODIC SOLUTIONS OF SOME VOLTERRA INTEGRAL EQUATIONS
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BibTeX
@MISC{Cushing_nontrivialperiodic,
author = {J. M. Cushing},
title = {NONTRIVIAL PERIODIC SOLUTIONS OF SOME VOLTERRA INTEGRAL EQUATIONS},
year = {}
}
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Abstract
I. Introductory Remarks. My main purpose in this paper is to prove a bifurcation theorem for nontrivial periodic solutions of a general system of Volterra integral equations. The motivation for considering this problem can be found in models which arise in population dynamics, epidemiology and economics [1,3,6], an example of which appears in §5. The approach taken is that which is usually referred to as the method of Liapunov-Schmidt (or often called ~he method of alternative problems). This method, which is applicable in a very general setting, is outlined in §2 in a way suitable for the type of problems I have in mind. The fundamental ingredient for this approach in its application to many problems is a Fredholm alternative. A Fredholm alternative for systems of Volterra integral equations is proved in §3. The main bifurcation result (Theorem 4) appears in §4 and an application is given in §5 to a scalar model which has arisen in the mathematical theory of population growth and of epidemics. 2. Some General Remarks. spaces and suppose L:X-~Y
Keyphrases
fredholm alternative volterra integral equation nontrivial periodic solution alternative problem bifurcation theorem main bifurcation result mathematical theory population growth general system population dynamic general remark general setting scalar model introductory remark many problem fundamental ingredient main purpose
