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Bounded and Almost-Periodic Solutions of Nonlocal Perturbations of Nonautonomous Logistic-Type Equations

Bounded and Almost-Periodic Solutions of Nonlocal Perturbations of Nonautonomous Logistic-Type... This paper is concerned with the study of dynamics of nonlinear nonlocal perturbations of nonautonomous logistic-type equations. More specifically, we prove the existence and uniqueness of a bounded solution that is positive, and that does not approach the zero solution in the past and in the future. We also show that this solution is an attractor for all other positive solutions. Since the zero solution is shown to be a repeller for all solutions that remain below the aforementioned one, we obtain an attractor-repeller pair. Almost-periodic attractor is also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Bounded and Almost-Periodic Solutions of Nonlocal Perturbations of Nonautonomous Logistic-Type Equations

Acta Applicandae Mathematicae , Volume 65 (3) – Oct 19, 2004

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References (29)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1010626231398
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the study of dynamics of nonlinear nonlocal perturbations of nonautonomous logistic-type equations. More specifically, we prove the existence and uniqueness of a bounded solution that is positive, and that does not approach the zero solution in the past and in the future. We also show that this solution is an attractor for all other positive solutions. Since the zero solution is shown to be a repeller for all solutions that remain below the aforementioned one, we obtain an attractor-repeller pair. Almost-periodic attractor is also discussed.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 19, 2004

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