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An application of topological degree to the periodic competing species problem

Published online by Cambridge University Press:  17 February 2009

Carlos Alvarez  and
Alan C. Lazer
Carlos Alvarez
Affiliation:
Departmento de Mathematicas, Facultad de Ciencias, Universidad de Los Andes, Merida, Venezuela
Alan C. Lazer
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Fla., 33124, U.S.A.
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Abstract

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We consider the Volterra-Lotka equations for two competing species in which the right-hand sides are periodic in time. Using topological degree, we show that conditions recently given by K. Gopalsamy, which imply the existence of a periodic solution with positive components, also imply the uniqueness and asymptotic stability of the solution. We also give optimal upper and lower bounds for the components of the solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 2 , October 1986 , pp. 202 - 219
Copyright
Copyright © Australian Mathematical Society 1986

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