Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Diffusive logistic equation with constant yield harvesting, I: Steady States


Authors: Shobha Oruganti, Junping Shi and Ratnasingham Shivaji
Journal: Trans. Amer. Math. Soc. 354 (2002), 3601-3619
MSC (2000): Primary 35J65; Secondary 35J25, 35B32, 92D25
Published electronically: May 7, 2002
MathSciNet review: 1911513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a reaction-diffusion equation which models the constant yield harvesting to a spatially heterogeneous population which satisfies a logistic growth. We prove the existence, uniqueness and stability of the maximal steady state solutions under certain conditions, and we also classify all steady state solutions under more restricted conditions. Exact global bifurcation diagrams are obtained in the latter case. Our method is a combination of comparison arguments and bifurcation theory.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J65, 35J25, 35B32, 92D25

Retrieve articles in all journals with MSC (2000): 35J65, 35J25, 35B32, 92D25


Additional Information

Shobha Oruganti
Affiliation: Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762
Email: so1@ra.msstate.edu

Junping Shi
Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187 and Department of Mathematics, Harbin Normal University, Harbin, Heilongjiang, P. R. China 150080
Email: shij@math.wm.edu

Ratnasingham Shivaji
Affiliation: Department of Mathematics, Mississippi State University, Mississippi State, Mississippi 39762
Email: shivaji@ra.msstate.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03005-2
Keywords: Diffusive logistic equation, harvesting, steady states, comparison methods, bifurcation
Received by editor(s): September 5, 2001
Received by editor(s) in revised form: October 15, 2001
Published electronically: May 7, 2002
Article copyright: © Copyright 2002 American Mathematical Society